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Консультация № 105399
14.10.2007, 12:16
0.00 руб.
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1
Добрый день
1. Даны вершины треугольной пирамиды ABCD. A(1,2,-7), B(-3,6,3), C(-2,7,3), D(-4,8,-12). Средствами векторной алгебры найти:
а)угол между ребрами AB и AD;
б)проекция ребра AD на ось ребра BC;
в)площадь треугольника BCD
г)высоту пирамиды ABCD, опущенную из вершины D на грань ABC.
2. Дано разложение векторов a и b по векторам p и c.
a=2p-3c, b=3p+c, p=4, c=1, (p^c)=П/6
Найти:
а)длины диагоналей параллелограмма, построенного на векторах a и b;
б)площадь этого параллелограмма;
в)угол между векторами a и b.
3. Коллинеарны ли векторы p и c, построенные по векторам a и b?
a=(7,9,-2), b=(5,4,3), p=4a-b, c=4b-a.
1. Даны вершины треугольной пирамиды ABCD. A(1,2,-7), B(-3,6,3), C(-2,7,3), D(-4,8,-12). Средствами векторной алгебры найти:
а)угол между ребрами AB и AD;
б)проекция ребра AD на ось ребра BC;
в)площадь треугольника BCD
г)высоту пирамиды ABCD, опущенную из вершины D на грань ABC.
2. Дано разложение векторов a и b по векторам p и c.
a=2p-3c, b=3p+c, p=4, c=1, (p^c)=П/6
Найти:
а)длины диагоналей параллелограмма, построенного на векторах a и b;
б)площадь этого параллелограмма;
в)угол между векторами a и b.
3. Коллинеарны ли векторы p и c, построенные по векторам a и b?
a=(7,9,-2), b=(5,4,3), p=4a-b, c=4b-a.
Обсуждение
Неизвестный
14.10.2007, 12:34
общий
это ответ
Здравствуйте, Ezhik!
№3.
p = 4a - b = 4*(7; 9; -2) - (5; 4; 3) = (23; 32; -11);
c = 4b - a = 4*(5; 4; 3) - (7; 9; -2) = (13; 7; 14).
23/13 ≠ 32/7 — векторы не коллинеарны.
Решения задач №2 и №3: http://webfile.ru/1555659.
Ответы ко второй и третьей задачам:
2. а) 2*sqrt(101-10*sqrt(3)) и 4*sqrt(2+sqrt(3));
2. б) S = 22;
2. в) arccos((93-14*sqrt(3))/sqrt(9721-2604*sqrt(3)));
3. векторы не коллинеарны.
№3.
p = 4a - b = 4*(7; 9; -2) - (5; 4; 3) = (23; 32; -11);
c = 4b - a = 4*(5; 4; 3) - (7; 9; -2) = (13; 7; 14).
23/13 ≠ 32/7 — векторы не коллинеарны.
Решения задач №2 и №3: http://webfile.ru/1555659.
Ответы ко второй и третьей задачам:
2. а) 2*sqrt(101-10*sqrt(3)) и 4*sqrt(2+sqrt(3));
2. б) S = 22;
2. в) arccos((93-14*sqrt(3))/sqrt(9721-2604*sqrt(3)));
3. векторы не коллинеарны.
Форма ответа
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