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Консультация № 199944
21.12.2020, 14:29
0.00 руб.
1
1
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Здравствуйте! У меня возникли сложности с таким вопросом:
"Найти расстояние от точки M0 до плоскости, проходящей через точки M1, M2, M3, если М1(0, -3, 1), М2(-4, 1, 2), М3(2, -1, 5), М0(-3, 4, -5)."
Есть скрин.
"Найти расстояние от точки M0 до плоскости, проходящей через точки M1, M2, M3, если М1(0, -3, 1), М2(-4, 1, 2), М3(2, -1, 5), М0(-3, 4, -5)."
Есть скрин.
Прикрепленные файлы:
Обсуждение
26.12.2020, 11:34
общий
это ответ
Здравствуйте, Alexander!
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: 7x + 9y - 8z + 35 = 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, 4, -5) до плоскости 7x + 9y - 8z + 35 = 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: 7x + 9y - 8z + 35 = 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, 4, -5) до плоскости 7x + 9y - 8z + 35 = 0 составит
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