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Консультация № 198038
24.03.2020, 21:13
0.00 руб.
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Найти расстояние от точки M0 до плоскости, проходящей через точки M1,M2,M3, если
Mi (-3, -5, 6), M2 (2, 1, -4), M3 (0, -3, -1), Mo (3, 6, 68).
Найти расстояние от точки M0 до плоскости, проходящей через точки M1,M2,M3, если
Mi (-3, -5, 6), M2 (2, 1, -4), M3 (0, -3, -1), Mo (3, 6, 68).
Обсуждение
29.03.2020, 08:15
общий
это ответ
Здравствуйте, master87!
Рассмотрим произвольную точку M(x, y, z), лежащую в одной плоскости с точками M[sub]1[/sub], M[sub]2[/sub], M[sub]3[/sub]. Очевидно, что любые три вектора с вершинами в этих точках, например,
также будут лежать в этой плоскости (будут компланарными), и их смешанное произведение будет равно нулю:
что даёт нам уравнение плоскости.
Для произвольной точки M[sub]0[/sub](x[sub]0[/sub], y[sub]0[/sub], z[sub]0[/sub]) расстояние от неё до плоскости, заданной уравнением Ax + By + Cz + D = 0, определяется выражением
В данном случае расстояние от точки M[sub]0[/sub](3, 6, 68) до плоскости -22x + 5y - 8z + 7 = 0 составит
Рассмотрим произвольную точку M(x, y, z), лежащую в одной плоскости с точками M[sub]1[/sub], M[sub]2[/sub], M[sub]3[/sub]. Очевидно, что любые три вектора с вершинами в этих точках, например,
также будут лежать в этой плоскости (будут компланарными), и их смешанное произведение будет равно нулю:
что даёт нам уравнение плоскости.
Для произвольной точки M[sub]0[/sub](x[sub]0[/sub], y[sub]0[/sub], z[sub]0[/sub]) расстояние от неё до плоскости, заданной уравнением Ax + By + Cz + D = 0, определяется выражением
В данном случае расстояние от точки M[sub]0[/sub](3, 6, 68) до плоскости -22x + 5y - 8z + 7 = 0 составит
5
Спасибо!!!
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