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Консультация № 194341
03.01.2019, 22:10
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Написать уравнение плоскости, проходящей через точки P и Q и перпендикулярной к заданной плоскости:
P(2, 1, -1); Q(4,-2, 1); 3x + 2y - 5z - 10=0.
Написать уравнение плоскости, проходящей через точки P и Q и перпендикулярной к заданной плоскости:
P(2, 1, -1); Q(4,-2, 1); 3x + 2y - 5z - 10=0.
Обсуждение
06.01.2019, 22:10
общий
это ответ
Здравствуйте, Valeriya!
Вектор
является нормальным вектором заданной плоскости. Пусть точка 
расположена в искомой плоскости. Тогда в искомой плоскости расположены векторы
и вектор
Смешанное произведение этих трёх векторов должно быть равно нулю; поэтому
-- общее уравнение искомой плоскости.
Вектор
является нормальным вектором заданной плоскости. Пусть точка расположена в искомой плоскости. Тогда в искомой плоскости расположены векторыи вектор
Смешанное произведение этих трёх векторов должно быть равно нулю; поэтому -- общее уравнение искомой плоскости.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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