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Консультация № 153204
06.12.2008, 14:52
0.00 руб.
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Уважаемые эксперты. Прошу помощи.
Даны точки A, B, C, D
A (4, 4, 10), B (4, 10, 2), C (2, 8, 4), D (9, 6, 4)
Показать, что эти точки не лежат в одной плоскости.
Заранее спасибо.
Даны точки A, B, C, D
A (4, 4, 10), B (4, 10, 2), C (2, 8, 4), D (9, 6, 4)
Показать, что эти точки не лежат в одной плоскости.
Заранее спасибо.
Обсуждение
Неизвестный
07.12.2008, 21:45
общий
это ответ
Здравствуйте, Александров Анатолий Олегович!
Чтобы показать, что точки не пренадлежат одной плоскости, надо показать, что вектора AB, AC, AD не компланарны
AB=(4-4, 10-4, 2-10)=(0, 6, -8)
AC=(2-4, 8-4, 4-10)=(-2, 4, -6)
AD=(9-4, 6-4, 4-10)=(5, 2, -6)
|0...6...-8|
|-2..4..-6|=0+32-180+160-0-72=-60 не равно 0, значит указанные точки не лежат в одной плоскости
|5...2..-6|
Чтобы показать, что точки не пренадлежат одной плоскости, надо показать, что вектора AB, AC, AD не компланарны
AB=(4-4, 10-4, 2-10)=(0, 6, -8)
AC=(2-4, 8-4, 4-10)=(-2, 4, -6)
AD=(9-4, 6-4, 4-10)=(5, 2, -6)
|0...6...-8|
|-2..4..-6|=0+32-180+160-0-72=-60 не равно 0, значит указанные точки не лежат в одной плоскости
|5...2..-6|
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