math-public:la-vektornyi-metod1
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| math-public:la-vektornyi-metod1 [2016/10/31 14:44] – создано labreslav | math-public:la-vektornyi-metod1 [2020/10/13 22:56] (текущий) – labreslav | ||
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| + | ===== Контрольное домашнее задание ===== | ||
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| + | ==== Требования к оформлению ==== | ||
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| + | Работа должна быть оформлена с титульным листом. | ||
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| + | Задачи должны быть оформлены по порядку. | ||
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| + | Все ответы должны быть максимально упрощены, | ||
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| + | На титульном листе должна быть оформлена таблица ответов по образцу: | ||
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| + | ^ |→p| | ||
| + | | \\ | | | | | | | | | | | | | | | ||
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| + | Номер своего варианта - ваш номер по списку. | ||
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| + | ==== Условия задач по вариантам ==== | ||
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| + | ^Вариант^Дано^Найти| | ||
| + | | 1. | |→a|=4; |→b|=4; cos(^→a;→b)=12;→p=43→a+43→b;→q=35→a+32→b;→m=x→a−34→b, →m⊥→q;→u=y→a−32→b; →v=34→a+y→b; →u⊥→v|−5→a+→d|=√421; |4→a+4→d|=4√13;|→c|=5; |−2→b+2→c|=2√1293;|−5→a−5→n|=5√51; (−2→a+2→n)(−2→a+5→n)=244; | ||
| + | | 2. | |→a|=3; |→b|=3; cos(^→a;→b)=−34;→p=−→a+→b;→q=12→a+→b;→m=x→a+52→b, →m⊥→q;→u=y→a−→b; →v=−13→a+y→b; →u⊥→v|−3→a−3→d|=3√37; |−5→a+2→d|=13;|→c|=4; |3→b−2→c|=√217;|5→a+2→n|=√151; (4→a−2→n)(→a−3→n)=123 | ||
| + | | 3. | |→a|=1; |→b|=2; cos(^→a;→b)=23;→p=−53→a−12→b;→q=−→a+12→b;→m=x→a+35→b, →m⊥→q;→u=y→a+2→b; →v=−2→a+y→b; →u⊥→v|−4→a+→d|=√8655; |4→a+→d|=√3855;|→c|=4; |−5→b−→c|=4√6;|−2→a−→n|=3; (2→a−5→n)(−2→a−5→n)=221; | ||
| + | | 4. | |→a|=1; |→b|=4; cos(^→a;→b)=−12;→p=→a+15→b;→q=→a+13→b;→m=x→a+→b, →m⊥→q;→u=y→a+45→b; →v=−4→a+y→b; →u⊥→v|2→a−4→d|=2√73; |−5→a+→d|=√61;|→c|=4; |−4→b−3→c|=4√33;|2→a+2→n|=√2; (−4→a+2→n)(−3→a−4→n)=−72; | ||
| + | | 5. | |→a|=3; |→b|=2; cos(^→a;→b)=12;→p=35→a−→b;→q=15→a+34→b;→m=x→a−23→b, →m⊥→q;→u=y→a+2→b; →v=→a+y→b; →u⊥→v|−4→a+3→d|=3√9855; |−5→a+5→d|=12√5;|→c|=1; |−5→b+4→c|=2√1413;|2→a+4→n|=2√37; (−3→a+3→n)(−5→a−5→n)=−105; | ||
| + | | 6. | |→a|=1; |→b|=4; cos(^→a;→b)=−45;→p=→a+34→b;→q=25→a+15→b;→m=x→a−45→b, →m⊥→q;→u=y→a−52→b; →v=45→a+y→b; →u⊥→v|→a−→d|=√2; |−2→a+4→d|=2√11;|→c|=4; |2→b+2→c|=16√105;|4→a−→n|=√3055; (−5→a+5→n)(5→a−3→n)=−16; | ||
| + | | 7. | |→a|=4; |→b|=3; cos(^→a;→b)=−12;→p=→a−13→b;→q=52→a+32→b;→m=x→a−54→b, →m⊥→q;→u=y→a+5→b; →v=−5→a+y→b; →u⊥→v|→a−5→d|=√301; |2→a+→d|=7;|→c|=1; |−5→b−5→c|=4√10;|2→a+2→n|=4√2055; (−→a+4→n)(−5→a+→n)=−1925; | ||
| + | | 8. | |→a|=1; |→b|=2; cos(^→a;→b)=34;→p=−54→a+52→b;→q=→a+34→b;→m=x→a+2→b, →m⊥→q;→u=y→a−3→b; →v=→a+y→b; →u⊥→v|−2→a−→d|=2√3; |−4→a+→d|=4√3;|→c|=1; |3→b+4→c|=2√22;|2→a+4→n|=14√213; (−5→a−3→n)(−→a−→n)=3203; | ||
| + | | 9. | |→a|=4; |→b|=4; cos(^→a;→b)=−12;→p=→a+12→b;→q=12→a−5→b;→m=x→a−34→b, →m⊥→q;→u=y→a+→b; →v=12→a+y→b; →u⊥→v|−→a+5→d|=2√39; |−→a+4→d|=4√7;|→c|=4; |→b+→c|=8√55;|4→a−2→n|=10; (2→a+4→n)(−2→a−5→n)=−852; | ||
| + | | 10. | |→a|=2; |→b|=1; cos(^→a;→b)=−12;→p=25→a+32→b;→q=12→a+43→b;→m=x→a−53→b, →m⊥→q;→u=y→a+53→b; →v=−→a+y→b; →u⊥→v|3→a−3→d|=12√55; |−3→a−2→d|=2√5055;|→c|=3; |−4→b+3→c|=√9855;|−3→a+2→n|=√46; (2→a+→n)(−5→a−5→n)=−752; | ||
| + | | 11. | |→a|=1; |→b|=5; cos(^→a;→b)=−45;→p=−5→a+→b;→q=−→a+→b;→m=x→a+23→b, →m⊥→q;→u=y→a−5→b; →v=−12→a+y→b; →u⊥→v|→a−4→d|=3√17; |−3→a−4→d|=√129;|→c|=2; |−3→b+2→c|=√301;|2→a+2→n|=2√2655; (−2→a+3→n)(−4→a−3→n)=−5845; | ||
| + | | 12. | |→a|=1; |→b|=4; cos(^→a;→b)=−23;→p=53→a−5→b;→q=−→a+3→b;→m=x→a−14→b, →m⊥→q;→u=y→a+34→b; →v=13→a+y→b; →u⊥→v|→a+4→d|=√411; |2→a−2→d|=√94;|→c|=2; |−4→b−5→c|=2√29;|4→a+4→n|=8√2; (2→a+5→n)(−5→a−→n)=−28; | ||
| + | | 13. | |→a|=3; |→b|=1; cos(^→a;→b)=−15;→p=2→a+2→b;→q=−12→a+52→b;→m=x→a+52→b, →m⊥→q;→u=y→a+54→b; →v=54→a+y→b; →u⊥→v|−→a+3→d|=3√742; |−3→a+3→d|=3√462;|→c|=1; |−→b−2→c|=√1655;|→a+4→n|=3√23; (−3→a+3→n)(2→a+→n)=−274; | ||
| + | | 14. | |→a|=2; |→b|=3; cos(^→a;→b)=−45;→p=−12→a−53→b;→q=−→a−43→b;→m=x→a+3→b, →m⊥→q;→u=y→a+→b; →v=32→a+y→b; →u⊥→v|5→a−5→d|=10√7; |−5→a−5→d|=10√3;|→c|=1; |2→b−4→c|=2√7;|3→a+4→n|=2√19; (−2→a−5→n)(5→a+5→n)=−100; | ||
| + | | 15. | |→a|=4; |→b|=1; cos(^→a;→b)=−45;→p=−→a−2→b;→q=−→a−54→b;→m=x→a−15→b, →m⊥→q;→u=y→a−→b; →v=−43→a+y→b; →u⊥→v|−5→a−3→d|=5√33; |−2→a+4→d|=4√2013;|→c|=2; |−→b+→c|=√3;|→a+→n|=2√7; (−→a−→n)(3→a+2→n)=−76; | ||
| + | | 16. | |→a|=5; |→b|=5; cos(^→a;→b)=13;→p=13→a−12→b;→q=−23→a−→b;→m=x→a+54→b, →m⊥→q;→u=y→a−→b; →v=5→a+y→b; →u⊥→v|−3→a+→d|=5√7; |−3→a−2→d|=5√19;|→c|=3; |−2→b+3→c|=√271;|−2→a+4→n|=10√693; (4→a−→n)(4→a−5→n)=925; | ||
| + | | 17. | |→a|=2; |→b|=2; cos(^→a;→b)=−35;→p=−→a−45→b;→q=−→a+3→b;→m=x→a−53→b, →m⊥→q;→u=y→a+52→b; →v=−32→a+y→b; →u⊥→v|−4→a−→d|=√73; |3→a+5→d|=√601;|→c|=4; |−3→b−4→c|=2√15855;|−4→a+4→n|=4√855; (4→a−→n)(−4→a−4→n)=−3485; | ||
| + | | 18. | |→a|=2; |→b|=3; cos(^→a;→b)=13;→p=4→a−2→b;→q=25→a+25→b;→m=x→a−15→b, →m⊥→q;→u=y→a+5→b; →v=−5→a+y→b; →u⊥→v|3→a+→d|=2√6; |5→a−→d|=14√63;|→c|=3; |→b+3→c|=3√3105;|−2→a−→n|=√17; (2→a+3→n)(2→a+2→n)=106; | ||
| + | | 19. | |→a|=5; |→b|=1; cos(^→a;→b)=−45;→p=−32→a−5→b;→q=−23→a−13→b;→m=x→a+35→b, →m⊥→q;→u=y→a−35→b; →v=−→a+y→b; →u⊥→v|−4→a−3→d|=5√31; |→a−4→d|=5√15;|→c|=4; |−2→b+5→c|=2√8493;|−→a−4→n|=√137; (−→a−5→n)(5→a−3→n)=−197; | ||
| + | | 20. | |→a|=5; |→b|=2; cos(^→a;→b)=−34;→p=→a+2→b;→q=25→a−23→b;→m=x→a+2→b, →m⊥→q;→u=y→a+3→b; →v=25→a+y→b; →u⊥→v|−3→a+5→d|=15√142; |5→a−4→d|=√1219;|→c|=3; |−3→b−5→c|=√381;|−5→a−5→n|=25√102; (−3→a+2→n)(3→a−→n)=−8754; | ||
| + | | 21. | |→a|=5; |→b|=4; cos(^→a;→b)=25;→p=2→a+34→b;→q=25→a+3→b;→m=x→a−→b, →m⊥→q;→u=y→a+→b; →v=→a+y→b; →u⊥→v|5→a+5→d|=5√1662; |−5→a+5→d|=5√1062;|→c|=1; |3→b+2→c|=2√31;|2→a+2→n|=10; (−5→a+4→n)(−3→a−2→n)=200; | ||
| + | | 22. | |→a|=4; |→b|=3; cos(^→a;→b)=25;→p=35→a−→b;→q=−→a−52→b;→m=x→a+12→b, →m⊥→q;→u=y→a+43→b; →v=32→a+y→b; →u⊥→v|−4→a−4→d|=4√4655; |3→a−→d|=√35055;|→c|=5; |−2→b+2→c|=2√19;|4→a+2→n|=8√7; (→a+2→n)(−→a−4→n)=−192; | ||
| + | | 23. | |→a|=5; |→b|=1; cos(^→a;→b)=−15;→p=−2→a−43→b;→q=−12→a−13→b;→m=x→a−32→b, →m⊥→q;→u=y→a−53→b; →v=13→a+y→b; →u⊥→v|4→a+→d|=5√13; |2→a+4→d|=10√3;|→c|=5; |−3→b−5→c|=√709;|−→a−3→n|=√229; (3→a+2→n)(5→a−→n)=413; | ||
| + | | 24. | |→a|=5; |→b|=3; cos(^→a;→b)=12;→p=−→a−23→b;→q=35→a−12→b;→m=x→a+5→b, →m⊥→q;→u=y→a−→b; →v=−→a+y→b; →u⊥→v|→a−2→d|=√33; |−5→a+4→d|=√681;|→c|=4; |→b+5→c|=√349;|−3→a−3→n|=3√37; (2→a+5→n)(−→a+4→n)=42; | ||
| + | | 25. | |\vec{a}|=3;\ |\vec{b}|=3;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{1}{2};\\ \vec{p}=\vec{a}-\frac{1}{5}\vec{b};\\ \vec{q}=4\vec{a}-\frac{4}{5}\vec{b};\\ \vec{m}=x\vec{a}+\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\frac{4}{5}\vec{b};\ \vec{v}=3\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-5\vec{a}-3\vec{d}|=\sqrt{489};\ |-2\vec{a}-4\vec{d}|=2\sqrt{89};\\ |\vec{c}|=3;\ |-\vec{b}+4\vec{c}|=3\sqrt{21};\\ |-2\vec{a}-4\vec{n}|=2\sqrt{129};\ (-\vec{a}-4\vec{n})(-4\vec{a}-5\vec{n})=641; | ||
| + | | 26. | |\vec{a}|=5;\ |\vec{b}|=5;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{2}{3};\\ \vec{p}=-5\vec{a}-\vec{b};\\ \vec{q}=-\frac{3}{4}\vec{a}+\vec{b};\\ \vec{m}=x\vec{a}+2\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\frac{5}{3}\vec{b};\ \vec{v}=\frac{4}{5}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |3\vec{a}-4\vec{d}|=\sqrt{385};\ |-\vec{a}+3\vec{d}|=\sqrt{190};\\ |\vec{c}|=3;\ |2\vec{b}+3\vec{c}|=\sqrt{109};\\ |5\vec{a}-5\vec{n}|=15;\ (-\vec{a}+4\vec{n})(2\vec{a}-\vec{n})=30; | ||
| + | | 27. | |\vec{a}|=2;\ |\vec{b}|=2;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{3}{4};\\ \vec{p}=-\frac{5}{2}\vec{a}+3\vec{b};\\ \vec{q}=2\vec{a}+4\vec{b};\\ \vec{m}=x\vec{a}+\frac{3}{2}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\vec{b};\ \vec{v}=\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-2\vec{a}+\vec{d}|=2\sqrt{7};\ |3\vec{a}+5\vec{d}|=2\sqrt{19};\\ |\vec{c}|=2;\ |\vec{b}+2\vec{c}|=\dfrac{2\sqrt{185}}{5};\\ |-\vec{a}-3\vec{n}|=\sqrt{217};\ (3\vec{a}-2\vec{n})(2\vec{a}-\vec{n})=88; | ||
| + | | 28. | |\vec{a}|=2;\ |\vec{b}|=3;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{1}{5};\\ \vec{p}=-\frac{3}{5}\vec{a}+\frac{1}{2}\vec{b};\\ \vec{q}=-3\vec{a}-3\vec{b};\\ \vec{m}=x\vec{a}-5\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+\frac{1}{2}\vec{b};\ \vec{v}=-\frac{3}{4}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |4\vec{a}+\vec{d}|=8\sqrt{2};\ |-5\vec{a}-4\vec{d}|=2\sqrt{149};\\ |\vec{c}|=2;\ |5\vec{b}+3\vec{c}|=3\sqrt{33};\\ |-4\vec{a}+4\vec{n}|=4\sqrt{10};\ (4\vec{a}-\vec{n})(-3\vec{a}-\vec{n})=-43; | ||
| + | | 29. | |\vec{a}|=4;\ |\vec{b}|=1;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{1}{2};\\ \vec{p}=\frac{3}{4}\vec{a}-\frac{3}{2}\vec{b};\\ \vec{q}=-\frac{5}{2}\vec{a}+\frac{5}{3}\vec{b};\\ \vec{m}=x\vec{a}-\frac{5}{2}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+\frac{2}{5}\vec{b};\ \vec{v}=-\frac{2}{5}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |2\vec{a}-4\vec{d}|=\dfrac{8\sqrt{6}}{3};\ |-3\vec{a}+4\vec{d}|=4\sqrt{5};\\ |\vec{c}|=1;\ |\vec{b}+3\vec{c}|=\dfrac{\sqrt{190}}{5};\\ |-2\vec{a}-\vec{n}|=\dfrac{2\sqrt{305}}{5};\ (5\vec{a}-2\vec{n})(-\vec{a}-\vec{n})=-\frac{288}{5}; | ||
| + | | 30. | |\vec{a}|=2;\ |\vec{b}|=2;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{2}{3};\\ \vec{p}=-\frac{2}{3}\vec{a}+\vec{b};\\ \vec{q}=4\vec{a}+\frac{3}{2}\vec{b};\\ \vec{m}=x\vec{a}+2\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-2\vec{b};\ \vec{v}=5\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-\vec{a}-2\vec{d}|=2\sqrt{3};\ |4\vec{a}+3\vec{d}|=2\sqrt{13};\\ |\vec{c}|=1;\ |-2\vec{b}-5\vec{c}|=\sqrt{71};\\ |-5\vec{a}+\vec{n}|=2\sqrt{29};\ (4\vec{a}-4\vec{n})(-4\vec{a}+\vec{n})=-98; | ||
| + | | 31. | |\vec{a}|=3;\ |\vec{b}|=5;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{4}{5};\\ \vec{p}=-\frac{3}{4}\vec{a}+\vec{b};\\ \vec{q}=\frac{1}{2}\vec{a}-\frac{2}{3}\vec{b};\\ \vec{m}=x\vec{a}-\frac{5}{2}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+2\vec{b};\ \vec{v}=-\frac{2}{3}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-5\vec{a}-5\vec{d}|=6\sqrt{15};\ |-5\vec{a}-2\vec{d}|=3\sqrt{33};\\ |\vec{c}|=3;\ |3\vec{b}-5\vec{c}|=\dfrac{15\sqrt{10}}{2};\\ |5\vec{a}+\vec{n}|=\sqrt{145};\ (-4\vec{a}+4\vec{n})(\vec{a}-\vec{n})=-\frac{884}{5}; | ||
| + | | 32. | |\vec{a}|=5;\ |\vec{b}|=4;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{3}{4};\\ \vec{p}=4\vec{a}-5\vec{b};\\ \vec{q}=-\vec{a}-\frac{3}{2}\vec{b};\\ \vec{m}=x\vec{a}-\frac{3}{2}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-5\vec{b};\ \vec{v}=-\frac{2}{5}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-4\vec{a}-3\vec{d}|=2\sqrt{61};\ |-2\vec{a}-\vec{d}|=6\sqrt{2};\\ |\vec{c}|=3;\ |-3\vec{b}+3\vec{c}|=3\sqrt{13};\\ |\vec{a}+5\vec{n}|=\sqrt{70};\ (2\vec{a}+4\vec{n})(4\vec{a}+5\vec{n})=272; | ||
| + | | 33. | |\vec{a}|=1;\ |\vec{b}|=5;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{1}{3};\\ \vec{p}=-\vec{a}-\vec{b};\\ \vec{q}=-4\vec{a}+\frac{3}{2}\vec{b};\\ \vec{m}=x\vec{a}+\frac{5}{3}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+\frac{3}{5}\vec{b};\ \vec{v}=-\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-4\vec{a}+\vec{d}|=\dfrac{2\sqrt{205}}{5};\ |\vec{a}-4\vec{d}|=\dfrac{\sqrt{1945}}{5};\\ |\vec{c}|=2;\ |5\vec{b}+3\vec{c}|=\sqrt{511};\\ |4\vec{a}+\vec{n}|=\dfrac{\sqrt{145}}{5};\ (3\vec{a}-3\vec{n})(-4\vec{a}+4\vec{n})=-\frac{888}{5}; | ||
| + | | 34. | |\vec{a}|=1;\ |\vec{b}|=1;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{1}{2};\\ \vec{p}=-\frac{1}{2}\vec{a}+\frac{1}{4}\vec{b};\\ \vec{q}=-\vec{a}+\frac{5}{2}\vec{b};\\ \vec{m}=x\vec{a}-\frac{3}{5}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-5\vec{b};\ \vec{v}=5\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |3\vec{a}-2\vec{d}|=\dfrac{\sqrt{385}}{5};\ |5\vec{a}-\vec{d}|=\sqrt{21};\\ |\vec{c}|=3;\ |5\vec{b}+5\vec{c}|=5\sqrt{7};\\ |2\vec{a}-\vec{n}|=\sqrt{21};\ (-\vec{a}-4\vec{n})(4\vec{a}+\vec{n})=-6; | ||
| + | | 35. | |\vec{a}|=1;\ |\vec{b}|=4;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{3}{5};\\ \vec{p}=-4\vec{a}-2\vec{b};\\ \vec{q}=\frac{4}{3}\vec{a}-\vec{b};\\ \vec{m}=x\vec{a}+\frac{1}{2}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+\vec{b};\ \vec{v}=-\frac{3}{4}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-\vec{a}-\vec{d}|=\dfrac{\sqrt{69}}{3};\ |5\vec{a}-4\vec{d}|=\dfrac{\sqrt{321}}{3};\\ |\vec{c}|=1;\ |-\vec{b}+4\vec{c}|=4;\\ |-3\vec{a}+3\vec{n}|=\dfrac{3\sqrt{34}}{2};\ (-3\vec{a}-\vec{n})(4\vec{a}+\vec{n})=-\frac{105}{4}; | ||
| + | | 36. | |\vec{a}|=2;\ |\vec{b}|=4;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{2}{3};\\ \vec{p}=2\vec{a}+\vec{b};\\ \vec{q}=-\vec{a}-\frac{2}{3}\vec{b};\\ \vec{m}=x\vec{a}+4\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\vec{b};\ \vec{v}=\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-5\vec{a}+2\vec{d}|=2\sqrt{39};\ |4\vec{a}+4\vec{d}|=8;\\ |\vec{c}|=5;\ |3\vec{b}+5\vec{c}|=\sqrt{1009};\\ |5\vec{a}+5\vec{n}|=\dfrac{5\sqrt{69}}{3};\ (-2\vec{a}+4\vec{n})(-2\vec{a}-4\vec{n})=0; | ||
| + | | 37. | |\vec{a}|=5;\ |\vec{b}|=2;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{1}{3};\\ \vec{p}=-2\vec{a}+\frac{5}{3}\vec{b};\\ \vec{q}=-\frac{3}{4}\vec{a}+\frac{1}{4}\vec{b};\\ \vec{m}=x\vec{a}-4\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\frac{5}{3}\vec{b};\ \vec{v}=\frac{2}{5}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |-2\vec{a}+5\vec{d}|=5\sqrt{19};\ |-2\vec{a}-5\vec{d}|=5\sqrt{39};\\ |\vec{c}|=3;\ |\vec{b}-2\vec{c}|=\dfrac{4\sqrt{85}}{5};\\ |2\vec{a}+2\vec{n}|=2\sqrt{17};\ (4\vec{a}+4\vec{n})(4\vec{a}-3\vec{n})=160; | ||
| + | | 38. | |\vec{a}|=5;\ |\vec{b}|=3;\ \cos{(\hat{\vec{a};\vec{b}})}=\frac{1}{2};\\ \vec{p}=\frac{3}{5}\vec{a}-\frac{2}{3}\vec{b};\\ \vec{q}=-\vec{a}+\frac{4}{3}\vec{b};\\ \vec{m}=x\vec{a}-2\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}-\frac{4}{3}\vec{b};\ \vec{v}=\frac{2}{5}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |2\vec{a}-4\vec{d}|=2\sqrt{129};\ |2\vec{a}+\vec{d}|=2\sqrt{19};\\ |\vec{c}|=3;\ |5\vec{b}-5\vec{c}|=15\sqrt{3};\\ |3\vec{a}-5\vec{n}|=15;\ (2\vec{a}-4\vec{n})(-5\vec{a}-5\vec{n})=5; | ||
| + | | 39. | |\vec{a}|=2;\ |\vec{b}|=1;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{1}{3};\\ \vec{p}=\frac{1}{2}\vec{a}-\vec{b};\\ \vec{q}=\frac{3}{5}\vec{a}-\frac{3}{5}\vec{b};\\ \vec{m}=x\vec{a}-\frac{2}{3}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+3\vec{b};\ \vec{v}=-\frac{4}{3}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |3\vec{a}+\vec{d}|=\sqrt{31};\ |-3\vec{a}+\vec{d}|=\sqrt{43};\\ |\vec{c}|=1;\ |-2\vec{b}+4\vec{c}|=\dfrac{2\sqrt{65}}{5};\\ |-\vec{a}-2\vec{n}|=2\sqrt{23};\ (3\vec{a}-5\vec{n})(5\vec{a}+2\vec{n})=-214; | ||
| + | | 40. | |\vec{a}|=3;\ |\vec{b}|=1;\ \cos{(\hat{\vec{a};\vec{b}})}=-\frac{1}{5};\\ \vec{p}=\vec{a}+\vec{b};\\ \vec{q}=-\vec{a}-\frac{3}{2}\vec{b};\\ \vec{m}=x\vec{a}+\frac{2}{3}\vec{b},\ \vec{m}\perp\vec{q};\\ \\ \vec{u}=y\vec{a}+4\vec{b};\ \vec{v}=-\frac{4}{3}\vec{a}+y\vec{b};\ \vec{u}\perp\vec{v} \\ |2\vec{a}-2\vec{d}|=8;\ |2\vec{a}+\vec{d}|=\sqrt{34};\\ |\vec{c}|=2;\ |-2\vec{b}+\vec{c}|=\sqrt{2};\\ |3\vec{a}-2\vec{n}|=\dfrac{3\sqrt{565}}{5};\ (-2\vec{a}-3\vec{n})(2\vec{a}-\vec{n})=\frac{99}{5}; | ||
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math-public/la-vektornyi-metod1.1477914299.txt.bz2 · Последнее изменение: 2016/10/31 14:44 — labreslav