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Консультация № 180098
30.09.2010, 00:01
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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) А1(1,2,4) можно ли построить на векторах AB и AD и АА1 параллелепипед и если да то найти его объём.
A(1,2,3) B(0,3,2) D(1,0,1) А1(1,2,4) можно ли построить на векторах AB и AD и АА1 параллелепипед и если да то найти его объём.
Обсуждение
30.09.2010, 07:50
общий
это ответ
Здравствуйте, bestwick.
Находим координаты векторов:
AB = (0 – 1; 3 – 2; 2 – 3) = (-1; 1; -1),
AD = (1 – 1; 0 – 2; 1 – 3) = (0; -2; -2),
AA[sub]1[/sub] = (1 – 1; 2 – 2; 4 – 3) = (0; 0; 1).
Находим смешанное произведение векторов: {AB, AD, AA[sub]1[/sub]} =
|-1 1 -1|
|0 -2 -2| = (-1) ∙ (-2) ∙ 1 = 2 ≠ 0,
|0 0 1|
следовательно, параллелепипед построить можно, и его объем равен 2.
С уважением.
Находим координаты векторов:
AB = (0 – 1; 3 – 2; 2 – 3) = (-1; 1; -1),
AD = (1 – 1; 0 – 2; 1 – 3) = (0; -2; -2),
AA[sub]1[/sub] = (1 – 1; 2 – 2; 4 – 3) = (0; 0; 1).
Находим смешанное произведение векторов: {AB, AD, AA[sub]1[/sub]} =
|-1 1 -1|
|0 -2 -2| = (-1) ∙ (-2) ∙ 1 = 2 ≠ 0,
|0 0 1|
следовательно, параллелепипед построить можно, и его объем равен 2.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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