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Консультация № 200248
09.02.2021, 16:57
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Найти расстояние от точки M0 до плоскости, проходящей через точки M1,M2,M3, если
M1 (1;-1;2), M2 (2; 1;2), M3 (1;1;4), M4 (-3;2;7).
Найти расстояние от точки M0 до плоскости, проходящей через точки M1,M2,M3, если
M1 (1;-1;2), M2 (2; 1;2), M3 (1;1;4), M4 (-3;2;7).
Прикрепленные файлы:
Обсуждение
14.02.2021, 07:39
общий
это ответ
Здравствуйте, ALX5!
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:
Сократив последнее равенство на 2, получим уравнение плоскости: 2x - y + z - 5 = 0.
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, 2, 7) до плоскости 2x - y + z - 5 = 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:
Сократив последнее равенство на 2, получим уравнение плоскости: 2x - y + z - 5 = 0.
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, 2, 7) до плоскости 2x - y + z - 5 = 0 составит
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