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Консультация № 180093
29.09.2010, 21:01
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Добрый вечер уважаемые эксперты , помогите пожалуйста с решением задачи :
A(1,2,3) B(0,3,2) D(1,0,1) можно ли построить на векторах AB и AD параллелограмм и
A(1,2,3) B(0,3,2) D(1,0,1) можно ли построить на векторах AB и AD параллелограмм и
Обсуждение
29.09.2010, 21:57
общий
это ответ
Здравствуйте, bestwick.
AB={-1;1;-1}
AD={0;-2;-2}
Так как эти векторы не коллинеарны, то параллелограмм построить можно.
AB={-1;1;-1}
AD={0;-2;-2}
Так как эти векторы не коллинеарны, то параллелограмм построить можно.
29.09.2010, 23:11
общий
это ответ
Здравствуйте, bestwick.
Если векторы не коллинеарны, т. е. прямые, на которых эти векторы лежат, непараллельны, то на них можно построить параллелограмм. Чтобы убедиться в том, что векторы, образующие параллелограмм, не являются параллельными, найдем их координаты. Получим
AB = (0 - 1; 3 - 2; 2 - 3) = (-1; 1; -1),
AD = (1 - 1; 0 - 2; 1 - 3) = (0; -2; -2).
Поскольку -1/0 [$8800$] 1/(-2) [$8800$] -1/(-2), т. е. координаты векторов непропорциональны, то векторы не являются коллинеарными и могут являться сторонами параллелограмма. На векторах AB и AD можно построить параллелограмм.
Ответ: можно.
Если векторы не коллинеарны, т. е. прямые, на которых эти векторы лежат, непараллельны, то на них можно построить параллелограмм. Чтобы убедиться в том, что векторы, образующие параллелограмм, не являются параллельными, найдем их координаты. Получим
AB = (0 - 1; 3 - 2; 2 - 3) = (-1; 1; -1),
AD = (1 - 1; 0 - 2; 1 - 3) = (0; -2; -2).
Поскольку -1/0 [$8800$] 1/(-2) [$8800$] -1/(-2), т. е. координаты векторов непропорциональны, то векторы не являются коллинеарными и могут являться сторонами параллелограмма. На векторах AB и AD можно построить параллелограмм.
Ответ: можно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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