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Задать вопрос экспертам

Консультация № 129781

30.03.2008, 20:44

0.00 руб.

0 1 1

Образование

Здравствуйте, уважаемые эксперты. Помогите пожалуйства решить примеры. А совсем запутался с ними, может быть вы поможите?

Даны векторы a=вектору AB, b=вектору CD.

A(10,9,0);B(9,8,1);C(8,7,1);D(7,6,0)

Найти:
1) векторы 2a+b и a-2b
2)модуль |2a+b| и |a-2b|
3)скалярное произведение (2a+b)*(a-2b)
4)векторное произведение [(2a+b),(a-2b)]
5)угол между векторами 2a+b и a-2b

Я бы и сам решил, но тут в трёхмерном представлении, а этого я ещё не изучал. Помогите ПОЖАЛУЙСТА, очень срочно надо...
Спасибо!

Обсуждение

Неизвестный

30.03.2008, 22:09

общий

это ответ

Здравствуйте, Felix!
a(-1; -1; 1)
b(-1; -1: -1)
1) 2a+b(-1*2-1: -1*2-1: 1*2-1) = (-3: -3: 1)
a-2b(-1-2*(-1); -1-2*(-1); 1-2*(-1))=(1; 1; 3)
2) |2a+b|=√(9+9+1)=√19
|a-2b|=√(1+1+9)=√11
3) (2a+b)*(a-2b)= -3 -3 +3 = -3
4)[(2a+b),(a-2b)]=(-3*3-1*1; 1*1+3*1; -3*1+3*1) = (-10; 4; 0)

5) cosa = (2a+b)*(a-2b)/(|2a+b|*|a-2b|) = -3/√209
a = arccos(-3/√209) = прибл 102 градуса

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