حلول الأسئلة
السؤال
أوجد قياس الزاوية بين كل متجهين في كلّ مما يأتي، قرب الناتج إلى أقرب عشر.
الحل
u=4i+3j,v=-5i-2j
164.9°
شاهد حلول جميع الاسئلة
حل أسئلة تدرب وحل المسائل
أوجد حاصل الضرب الداخلي للمتجهين v, u، ثم تحقق ممَّا إذا كانا متعامدين أم لا.
1) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22127.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22134.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22141.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22148.5%22%20x2%3D%22153.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22153.5%22%20x2%3D%22148.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
8؛ غير متعامدين.
2) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E9%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22127.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22134.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22141.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22148.5%22%20x2%3D%22153.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22153.5%22%20x2%3D%22148.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
0؛ متعامدان.
3) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22127.5%22%20y%3D%2216%22%3E7%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22134.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22141.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22148.5%22%20x2%3D%22153.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22153.5%22%20x2%3D%22148.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
8؛ غير متعامدين.
4) u=11i+7j,v =-7i+11j
0؛ متعامدان.
5) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2243.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2255.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2262.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22130.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22142.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22149.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22159.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22171.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22178.5%22%20x2%3D%22183.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22183.5%22%20x2%3D%22178.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
8؛ غير متعامدين.
6) زيت زيتون: يمثل المتجه
أعداد علبتين مختلفتين من زيت الزيتون في متجر، ويمثّل المتجه
سعر العلبة من كلا النوعين على الترتيب.
a) أوجد u · v.
15620
b) فسر النتيجة التي حصلت عليها في الفرع a في سياق المسألة.
ثمن العلب جميعها هو 15620 ريالاً.
استعمل الضرب الداخلي؛ لإيجاد طول المتجه المعطى.
7) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%226.5%22%20y%3D%2216%22%3Em%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2221.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2237.5%22%20x2%3D%2232.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2232.5%22%20x2%3D%2237.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2258.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2265.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2277.5%22%20y%3D%2216%22%3E11%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2288.5%22%20x2%3D%2293.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2293.5%22%20x2%3D%2288.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
8) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%223.5%22%20y%3D%2216%22%3Er%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2214.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2230.5%22%20x2%3D%2225.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2225.5%22%20x2%3D%2230.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2239.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2251.5%22%20y%3D%2216%22%3E9%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2258.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2268.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2280.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2287.5%22%20x2%3D%2292.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2292.5%22%20x2%3D%2287.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
9) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2233.5%22%20x2%3D%2228.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2228.5%22%20x2%3D%2233.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2239.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2256.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2273.5%22%20y%3D%2216%22%3E18%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2284.5%22%20x2%3D%2289.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2289.5%22%20x2%3D%2284.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
10) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%222.5%22%20y%3D%2216%22%3Et%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2213.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2224.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2224.5%22%20x2%3D%2229.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E23%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2251.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2261.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2278.5%22%20y%3D%2216%22%3E16%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2289.5%22%20x2%3D%2294.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2294.5%22%20x2%3D%2289.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
أوجد قياس الزاوية
بين المتجهين u, v في كلّ مما يأتي، وقرب الناتج إلى أقرب جزء من عشرة.
11) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E0%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22127.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22134.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22144.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22156.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22163.5%22%20x2%3D%22168.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22168.5%22%20x2%3D%22163.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
14.0°
12) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E7%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2259.5%22%20y%3D%2216%22%3E10%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2270.5%22%20x2%3D%2275.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2275.5%22%20x2%3D%2270.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2279.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2286.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2299.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22115.5%22%20x2%3D%22110.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22110.5%22%20x2%3D%22115.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22121.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22128.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22138.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22150.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22157.5%22%20x2%3D%22162.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22162.5%22%20x2%3D%22157.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
100.0°
13) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2243.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2255.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2262.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22121.5%22%20x2%3D%22116.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22116.5%22%20x2%3D%22121.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22127.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22134.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22144.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22161.5%22%20y%3D%2216%22%3E10%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22172.5%22%20x2%3D%22177.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22177.5%22%20x2%3D%22172.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
164.7°
14) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2233.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2245.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2252.5%22%20y%3D%2216%22%3Ei%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2261.5%22%20y%3D%2216%22%3E%2B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2273.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2280.5%22%20y%3D%2216%22%3Ej%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2291.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22103.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22119.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22131.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22138.5%22%20y%3D%2216%22%3Ei%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1da2132f9123841445194c37573%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22147.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22159.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22166.5%22%20y%3D%2216%22%3Ej%3C%2Ftext%3E%3C%2Fsvg%3E)
82.9°
15) مخيم كشفي: غادر يوسف ويحيى مخيمهما الكشفي للبحث عن حطب، إذا كان المتجه
يمثل الطريق الذي سلكه يوسف، والمتجه
يمثل الطريق الذي سلكه يحيى، فأوجد قياس الزاوية بين المتجهين.
161.6°
16) فيزياء: يدفع طارق برميلاً على أرض مستوية مسافة 1.5 m بقوة مقدارها 534 N؛ بزاوية °25، أوجد مقدار الشغل بالجول الذي يبذله طارق، وقرب الناتج إلى أقرب عدد صحيح.
726J
أوجد متجهاً يعامد المتجه المعطى في كل مما يأتي:
17) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%227.5%22%20x2%3D%222.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%227.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2216.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2228.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2235.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2245.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E8%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2264.5%22%20x2%3D%2269.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2269.5%22%20x2%3D%2264.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
18) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%227.5%22%20x2%3D%222.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%227.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2213.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1f7177163c833dff4b38fc8d287%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2220.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2227.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2239.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2239.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
19) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%227.5%22%20x2%3D%222.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%227.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2213.5%22%20y%3D%2216%22%3E7%3C%2Ftext%3E%3Ctext%20font-family%3D%22math189201d0dea031dbbb328557e9a%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2220.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math189201d0dea031dbbb328557e9a%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2230.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2242.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2249.5%22%20x2%3D%2254.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2254.5%22%20x2%3D%2249.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
20) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%227.5%22%20x2%3D%222.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%227.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2216.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2228.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2235.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2242.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2249.5%22%20x2%3D%2254.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2254.5%22%20x2%3D%2249.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
21) عجلة دوارة: يعامد المتجه r في العجلة الدوارة في الوضع القياسي متجه السرعة المماسية v عند أيّ نقطة من نقاط الدائرة.
a) إذا كان طول نصف قطر العجلة 20 ft، وسرعتها ثابتة ومقدارها 40 ft/s، فاكتب الصورة الإحداثية للمتجه r في الوضع القياسي، إذا كان يصنع زاوية قياسها °35 مع الأفقي، فاكتب الصورة الإحداثية لمتجه السرعة المماسية في هذه الحالة؟ قرب الناتج إلى أقرب جزء من مئة.
(16.38, 11.47), (22.94, – 32.77)
b) ما الطريقة التي يمكن استعمالها لإثبات تعامد المتجه r، ومتجه السرعة باستعمال الصورتين الإحداثيتين اللتين أوجدتهما في
الفرع a؟ وأثبت أن المتجهين متعامدان.
(20 cos 35˚) (40 cos 35˚) + (20 sin 35˚) (– 40 sin 55˚) = 0
إذا علمت كلاً من v,u·v، فأوجد قيمة ممكنة للمتجه u في كلّ مما يأتي:
22) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A'stixf4d87ed3b0dbf9c79746d00cedb'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAANAIAAAwBQT1MvMi8nBU0AAADcAAAATmNtYXDCjdaBAAABLAAAADRjdnQgSG4BcAAAAWAAAADYZnBnbUUgjnwAAAI4AAANbWdseWYcKO%2BSAAAPqAAAADtoZWFkDLPdGwAAD%2BQAAAA2aGhlYQjYEyQAABAcAAAAJGhtdHg0LeORAAAQQAAAAAhsb2NhTQ9wLwAAEEgAAAAMbWF4cBlhFX0AABBUAAAAIG5hbWV4T00CAAAQdAAAAZ5wb3N0AgIA%2FwAAEhQAAAAgcHJlcFWzoI8AABI0AAAAvAAAApwBkAAFAAAD6APoAAAAAAPoA%2BgAAAAAAAEA%2BgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgICAgAAAAINf%2FAqX%2BvQAAA%2F8B5gAAAAAAAgABAAEAAAAUAAMAAQAAABQABAAgAAAABAAEAAEAACLF%2F%2F8AACLF%2F%2F%2FdPAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFoAWgAcABwClgAAAcIAAP8nA%2F%2F%2BGgKk%2F%2FIBzP%2F2%2FyYD%2F%2F4aAFkAWQAgACAClgAAAqsBwv%2F2%2FycD%2F%2F4aAqT%2F8gKrAcz%2F9v8mA%2F%2F%2BGgBaAFoAHAAcApYAAAKrAcIAAP8nA%2F%2F%2BGgKk%2F%2FICqwHM%2F%2Fb%2FJgP%2F%2FhoAWgBaABwAHAKWAQ4CqwI6AVD%2F7AP%2F%2FhoCpP%2FyAqsCOv%2F2%2F%2BwD%2F%2F4aABgAGAAYABgD%2F%2F4aA%2F%2F%2BGrAALCCwAFVYRVkgIEu4AA5RS7AGU1pYsDQbsChZYGYgilVYsAIlYbkIAAgAY2MjYhshIbAAWbAAQyNEsgABAENgQi2wASywIGBmLbACLCBkILDAULAEJlqyKAELQ0VjRbAGRVghsAMlWVJbWCEjIRuKWCCwUFBYIbBAWRsgsDhQWCGwOFlZILEBC0NFY0VhZLAoUFghsQELQ0VjRSCwMFBYIbAwWRsgsMBQWCBmIIqKYSCwClBYYBsgsCBQWCGwCmAbILA2UFghsDZgG2BZWVkbsAIlsApDY7AAUliwAEuwClBYIbAKQxtLsB5QWCGwHkthuBAAY7AKQ2O4BQBiWVlkYVmwAStZWSOwAFBYZVlZLbADLCBFILAEJWFkILAFQ1BYsAUjQrAGI0IbISFZsAFgLbAELCMhIyEgZLEFYkIgsAYjQrAGRVgbsQELQ0VjsQELQ7AFYEVjsAMqISCwBkMgiiCKsAErsTAFJbAEJlFYYFAbYVJZWCNZIVkgsEBTWLABKxshsEBZI7AAUFhlWS2wBSywB0MrsgACAENgQi2wBiywByNCIyCwACNCYbACYmawAWOwAWCwBSotsAcsICBFILAMQ2O4BABiILAAUFiwQGBZZrABY2BEsAFgLbAILLIHDABDRUIqIbIAAQBDYEItsAkssABDI0SyAAEAQ2BCLbAKLCAgRSCwASsjsABDsAQlYCBFiiNhIGQgsCBQWCGwABuwMFBYsCAbsEBZWSOwAFBYZVmwAyUjYUREsAFgLbALLCAgRSCwASsjsABDsAQlYCBFiiNhIGSwJFBYsAAbsEBZI7AAUFhlWbADJSNhRESwAWAtsAwsILAAI0KyCwoDRVghGyMhWSohLbANLLECAkWwZGFELbAOLLABYCAgsA1DSrAAUFggsA0jQlmwDkNKsABSWCCwDiNCWS2wDywgsBBiZrABYyC4BABjiiNhsA9DYCCKYCCwDyNCIy2wECxLVFixBGREWSSwDWUjeC2wESxLUVhLU1ixBGREWRshWSSwE2UjeC2wEiyxABBDVVixEBBDsAFhQrAPK1mwAEOwAiVCsQ0CJUKxDgIlQrABFiMgsAMlUFixAQBDYLAEJUKKiiCKI2GwDiohI7ABYSCKI2GwDiohG7EBAENgsAIlQrACJWGwDiohWbANQ0ewDkNHYLACYiCwAFBYsEBgWWawAWMgsAxDY7gEAGIgsABQWLBAYFlmsAFjYLEAABMjRLABQ7AAPrIBAQFDYEItsBMsALEAAkVUWLAQI0IgRbAMI0KwCyOwBWBCIGCwAWG1EhIBAA8AQkKKYLESBiuwiSsbIlktsBQssQATKy2wFSyxARMrLbAWLLECEystsBcssQMTKy2wGCyxBBMrLbAZLLEFEystsBossQYTKy2wGyyxBxMrLbAcLLEIEystsB0ssQkTKy2wKSwjILAQYmawAWOwBmBLVFgjIC6wAV0bISFZLbAqLCMgsBBiZrABY7AWYEtUWCMgLrABcRshIVktsCssIyCwEGJmsAFjsCZgS1RYIyAusAFyGyEhWS2wHiwAsA0rsQACRVRYsBAjQiBFsAwjQrALI7AFYEIgYLABYbUSEgEADwBCQopgsRIGK7CJKxsiWS2wHyyxAB4rLbAgLLEBHistsCEssQIeKy2wIiyxAx4rLbAjLLEEHistsCQssQUeKy2wJSyxBh4rLbAmLLEHHistsCcssQgeKy2wKCyxCR4rLbAsLCA8sAFgLbAtLCBgsBJgIEMjsAFgQ7ACJWGwAWCwLCohLbAuLLAtK7AtKi2wLywgIEcgILAMQ2O4BABiILAAUFiwQGBZZrABY2AjYTgjIIpVWCBHICCwDENjuAQAYiCwAFBYsEBgWWawAWNgI2E4GyFZLbAwLACxAAJFVFixDAtFQrABFrAvKrEFARVFWDBZGyJZLbAxLACwDSuxAAJFVFixDAtFQrABFrAvKrEFARVFWDBZGyJZLbAyLCA1sAFgLbAzLACxDAtFQrABRWO4BABiILAAUFiwQGBZZrABY7ABK7AMQ2O4BABiILAAUFiwQGBZZrABY7ABK7AAFrQAAAAAAEQ%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%2FKy2wdyyxADsrsEArLbB4LLEBOyuwPistsHkssQE7K7A%2FKy2weiyxATsrsEArLbB7LLEAPCsusS4BFCstsHwssQA8K7A%2BKy2wfSyxADwrsD8rLbB%2BLLEAPCuwQCstsH8ssQE8K7A%2BKy2wgCyxATwrsD8rLbCBLLEBPCuwQCstsIIssQA9Ky6xLgEUKy2wgyyxAD0rsD4rLbCELLEAPSuwPystsIUssQA9K7BAKy2whiyxAT0rsD4rLbCHLLEBPSuwPystsIgssQE9K7BAKy2wiSyzCQQCA0VYIRsjIVlCK7AIZbADJFB4sQUBFUVYMFktAAAAAAEAUwDBAMsBOQAHABhAFQABAAABVwABAQBfAAABAE8TEgILFisSFAYiJjQ2MssjMCUlMAEVMCQlLiUAAAEAAAABAAAzmKlrXw889QADA%2Bj%2F%2F%2F%2F%2F1GNNDf%2F%2F%2F%2F%2FUY00N%2FDb%2BGgigA%2F8AAAAKAAIAAQAAAAAAAQAAA%2F%2F%2BGgAACPj8Nv3JCKAAAQAAAAAAAAAAAAAAAAAAAAIA%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%2FAP8AAAAAAAAAAAAAAAAAAAAAAAAAAABLuADIUlixAQGOWbABuQgACABjcLEAB0K2AF9LNyMFACqxAAdCQAxmAlIIPggqCBgHBQgqsQAHQkAMagBcBkgGNAYhBQUIKrEADEK%2BGcAUwA%2FACsAGQAAFAAkqsQARQr4AQABAAEAAQABAAAUACSqxAwBEsSQBiFFYsECIWLEDAESxJgGIUVi6CIAAAQRAiGNUWLEDAERZWVlZQAxoAlQIQAgsCBoHBQwquAH%2FhbAEjbECAESzBWQGAERE)format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2233.5%22%20x2%3D%2228.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2228.5%22%20x2%3D%2233.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2239.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2256.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2268.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2275.5%22%20x2%3D%2280.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2280.5%22%20x2%3D%2275.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22stixf4d87ed3b0dbf9c79746d00cedb%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22101.5%22%20y%3D%2216%22%3E%26%23x22C5%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%22111.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math164afa8eacc29041f17144b9f42%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22124.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22142.5%22%20y%3D%2216%22%3E33%3C%2Ftext%3E%3C%2Fsvg%3E)
u = (5, – 3)
23) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A'stixf4d87ed3b0dbf9c79746d00cedb'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAANAIAAAwBQT1MvMi8nBU0AAADcAAAATmNtYXDCjdaBAAABLAAAADRjdnQgSG4BcAAAAWAAAADYZnBnbUUgjnwAAAI4AAANbWdseWYcKO%2BSAAAPqAAAADtoZWFkDLPdGwAAD%2BQAAAA2aGhlYQjYEyQAABAcAAAAJGhtdHg0LeORAAAQQAAAAAhsb2NhTQ9wLwAAEEgAAAAMbWF4cBlhFX0AABBUAAAAIG5hbWV4T00CAAAQdAAAAZ5wb3N0AgIA%2FwAAEhQAAAAgcHJlcFWzoI8AABI0AAAAvAAAApwBkAAFAAAD6APoAAAAAAPoA%2BgAAAAAAAEA%2BgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgICAgAAAAINf%2FAqX%2BvQAAA%2F8B5gAAAAAAAgABAAEAAAAUAAMAAQAAABQABAAgAAAABAAEAAEAACLF%2F%2F8AACLF%2F%2F%2FdPAABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFoAWgAcABwClgAAAcIAAP8nA%2F%2F%2BGgKk%2F%2FIBzP%2F2%2FyYD%2F%2F4aAFkAWQAgACAClgAAAqsBwv%2F2%2FycD%2F%2F4aAqT%2F8gKrAcz%2F9v8mA%2F%2F%2BGgBaAFoAHAAcApYAAAKrAcIAAP8nA%2F%2F%2BGgKk%2F%2FICqwHM%2F%2Fb%2FJgP%2F%2FhoAWgBaABwAHAKWAQ4CqwI6AVD%2F7AP%2F%2FhoCpP%2FyAqsCOv%2F2%2F%2BwD%2F%2F4aABgAGAAYABgD%2F%2F4aA%2F%2F%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%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%2FKy2wdyyxADsrsEArLbB4LLEBOyuwPistsHkssQE7K7A%2FKy2weiyxATsrsEArLbB7LLEAPCsusS4BFCstsHwssQA8K7A%2BKy2wfSyxADwrsD8rLbB%2BLLEAPCuwQCstsH8ssQE8K7A%2BKy2wgCyxATwrsD8rLbCBLLEBPCuwQCstsIIssQA9Ky6xLgEUKy2wgyyxAD0rsD4rLbCELLEAPSuwPystsIUssQA9K7BAKy2whiyxAT0rsD4rLbCHLLEBPSuwPystsIgssQE9K7BAKy2wiSyzCQQCA0VYIRsjIVlCK7AIZbADJFB4sQUBFUVYMFktAAAAAAEAUwDBAMsBOQAHABhAFQABAAABVwABAQBfAAABAE8TEgILFisSFAYiJjQ2MssjMCUlMAEVMCQlLiUAAAEAAAABAAAzmKlrXw889QADA%2Bj%2F%2F%2F%2F%2F1GNNDf%2F%2F%2F%2F%2FUY00N%2FDb%2BGgigA%2F8AAAAKAAIAAQAAAAAAAQAAA%2F%2F%2BGgAACPj8Nv3JCKAAAQAAAAAAAAAAAAAAAAAAAAIA%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%2FAP8AAAAAAAAAAAAAAAAAAAAAAAAAAABLuADIUlixAQGOWbABuQgACABjcLEAB0K2AF9LNyMFACqxAAdCQAxmAlIIPggqCBgHBQgqsQAHQkAMagBcBkgGNAYhBQUIKrEADEK%2BGcAUwA%2FACsAGQAAFAAkqsQARQr4AQABAAEAAQABAAAUACSqxAwBEsSQBiFFYsECIWLEDAESxJgGIUVi6CIAAAQRAiGNUWLEDAERZWVlZQAxoAlQIQAgsCBoHBQwquAH%2FhbAEjbECAESzBWQGAERE)format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10ebb3c113d02fd51a017c38df2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2216.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2232.5%22%20x2%3D%2227.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2227.5%22%20x2%3D%2232.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2238.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10ebb3c113d02fd51a017c38df2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2245.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2252.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2259.5%22%20x2%3D%2264.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2264.5%22%20x2%3D%2259.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math10ebb3c113d02fd51a017c38df2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2268.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2275.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22stixf4d87ed3b0dbf9c79746d00cedb%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2216%22%3E%26%23x22C5%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2294.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10ebb3c113d02fd51a017c38df2%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22106.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22124.5%22%20y%3D%2216%22%3E38%3C%2Ftext%3E%3C%2Fsvg%3E)
u = (– 1, 7)
24) مدرسة: يسحب طالب حقيبته المدرسية بقوة مقدارها 100 N، إذا بذل الطالب شغلاً مقداره 1747 J، لسحب حقيبته مسافة 31 m، فما قياس الزاوية بين قوة السحب والأفقي (بإهمال قوة الاحتكاك)؟
55.7 تقريباً.
اختبر كل زوج من المتجهات في كلّ مما يأتي، من حيث كونها متعامدة أو متوازية أو غير ذلك.
25) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2226%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2226%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2236.5%22%20y2%3D%2220.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2220.5%22%20y2%3D%224.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2243.5%22%20y%3D%2226%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2253.5%22%20x2%3D%2265.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2259.5%22%20y%3D%2215%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2259.5%22%20y%3D%2237%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2270.5%22%20y%3D%2226%22%3E%2C%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2275.5%22%20x2%3D%2287.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2281.5%22%20y%3D%2215%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2281.5%22%20y%3D%2237%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2292.5%22%20x2%3D%2297.5%22%20y1%3D%2236.5%22%20y2%3D%2220.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2297.5%22%20x2%3D%2292.5%22%20y1%3D%2220.5%22%20y2%3D%224.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22101.5%22%20y%3D%2226%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%22108.5%22%20y%3D%2226%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22121.5%22%20y%3D%2226%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22137.5%22%20x2%3D%22132.5%22%20y1%3D%2227.5%22%20y2%3D%2220.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22132.5%22%20x2%3D%22137.5%22%20y1%3D%2220.5%22%20y2%3D%2213.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22143.5%22%20y%3D%2226%22%3E9%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22150.5%22%20y%3D%2226%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22157.5%22%20y%3D%2226%22%3E8%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22164.5%22%20x2%3D%22169.5%22%20y1%3D%2227.5%22%20y2%3D%2220.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22169.5%22%20x2%3D%22164.5%22%20y1%3D%2220.5%22%20y2%3D%2213.5%22%2F%3E%3C%2Fsvg%3E)
متعامدان.
26) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2216%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2243.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2255.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2262.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2272.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2291.5%22%20x2%3D%2296.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2296.5%22%20x2%3D%2291.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22100.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%22107.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22120.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22136.5%22%20x2%3D%22131.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22131.5%22%20x2%3D%22136.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22142.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22149.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22156.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22163.5%22%20x2%3D%22168.5%22%20y1%3D%2217.5%22%20y2%3D%2210.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22168.5%22%20x2%3D%22163.5%22%20y1%3D%2210.5%22%20y2%3D%223.5%22%2F%3E%3C%2Fsvg%3E)
غير ذلك.
أوجد قياس الزاوية بين كل متجهين في كلّ مما يأتي، قرب الناتج إلى أقرب عشر.
27) u=i+5j,v=-2i+6j
29.7°
28) u=4i+3j,v=-5i-2j
164.9°
29) النقاط: (1,8) ,(7,4),(3,2) تمثّل رؤوس مثلث، أوجد قياسات زواياه باستعمال المتجهات.
37.8˚, 60.3˚, 81.9˚
إذا علمت كلاً من
والزاوية
بين المتجهين u,v، فأوجد قيمة ممكنة للمتجه v، قرب الناتج إلى أقرب جزء من مئة.
30) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2218%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2218%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2219.5%22%20y2%3D%2212.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2212.5%22%20y2%3D%225.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2218%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2218%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2218%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2218%22%3E2%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2276.5%22%20x2%3D%2281.5%22%20y1%3D%2219.5%22%20y2%3D%2212.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2281.5%22%20x2%3D%2276.5%22%20y1%3D%2212.5%22%20y2%3D%225.5%22%2F%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2285.5%22%20y%3D%2218%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2291.5%22%20y%3D%2218%22%3E%7C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2299.5%22%20y%3D%2218%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22107.5%22%20y%3D%2218%22%3E%7C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22119.5%22%20y%3D%2218%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22137.5%22%20y%3D%2218%22%3E10%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22148.5%22%20y%3D%2218%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%22155.5%22%20y%3D%2218%22%3E%26%23x3B8%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22169.5%22%20y%3D%2218%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22187.5%22%20y%3D%2218%22%3E45%3C%2Ftext%3E%3Ctext%20font-family%3D%22math16fd806a1dd48fd6b947fb97cc3%22%20font-size%3D%2212%22%20text-anchor%3D%22middle%22%20x%3D%22201.5%22%20y%3D%2212%22%3E%26%23x2218%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
(3.16, – 9.49)
31) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2219%22%3Eu%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2218.5%22%20y%3D%2219%22%3E%3D%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2234.5%22%20x2%3D%2229.5%22%20y1%3D%2220.5%22%20y2%3D%2213.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2229.5%22%20x2%3D%2234.5%22%20y1%3D%2213.5%22%20y2%3D%226.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2219%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2247.5%22%20y%3D%2219%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2254.5%22%20y%3D%2219%22%3E4%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2261.5%22%20x2%3D%2266.5%22%20y1%3D%2220.5%22%20y2%3D%2213.5%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2266.5%22%20x2%3D%2261.5%22%20y1%3D%2213.5%22%20y2%3D%226.5%22%2F%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2270.5%22%20y%3D%2219%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2276.5%22%20y%3D%2219%22%3E%7C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-weight%3D%22bold%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2219%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2292.5%22%20y%3D%2219%22%3E%7C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22104.5%22%20y%3D%2219%22%3E%3D%3C%2Ftext%3E%3Cpolyline%20fill%3D%22none%22%20points%3D%2212%2C-16%2011%2C-16%205%2C0%202%2C-6%22%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20transform%3D%22translate(113.5%2C20.5)%22%2F%3E%3Cpolyline%20fill%3D%22none%22%20points%3D%225%2C0%202%2C-6%200%2C-5%22%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20transform%3D%22translate(113.5%2C20.5)%22%2F%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%22125.5%22%20x2%3D%22146.5%22%20y1%3D%224.5%22%20y2%3D%224.5%22%2F%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22136.5%22%20y%3D%2219%22%3E29%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22149.5%22%20y%3D%2219%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%22156.5%22%20y%3D%2219%22%3E%26%23x3B8%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22170.5%22%20y%3D%2219%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22192.5%22%20y%3D%2219%22%3E121%3C%2Ftext%3E%3Ctext%20font-family%3D%22math104eedb8699c791907e82495b8b%22%20font-size%3D%2212%22%20text-anchor%3D%22middle%22%20x%3D%22211.5%22%20y%3D%2213%22%3E%26%23x2218%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
(– 5.36, 0.55)