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Консультация № 197490
24.12.2019, 15:00
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Задание 1. Написать уравнение плоскости, проходящей через точки P и Q и перпендикулярной к заданной плоскости:
P(-1,2,1); Q(3 ,-4 , 2); 2x + 4y - 3z + 5=0.
Задание 1. Написать уравнение плоскости, проходящей через точки P и Q и перпендикулярной к заданной плоскости:
P(-1,2,1); Q(3 ,-4 , 2); 2x + 4y - 3z + 5=0.
Обсуждение
29.12.2019, 04:08
общий
это ответ
Здравствуйте, i.gorkovenko123!
Из уравнения заданной плоскости 2x+4y-3z+5=0 определяем её нормальный вектор n = {2, 4, -3}, который, очевидно, лежит в плоскости, перпендикулярной к ней. Тогда для произвольной точки M(x, y, z) искомой плоскости вектора PM = {x+1, y-2, z-1}, PQ = {4, -6, 1} и n = {2, 4, -3} также лежат в этой плоскости, и их смешанное произведение равно 0:
откуда получаем искомое уравнение плоскости - x+y+2z-3=0.
Из уравнения заданной плоскости 2x+4y-3z+5=0 определяем её нормальный вектор n = {2, 4, -3}, который, очевидно, лежит в плоскости, перпендикулярной к ней. Тогда для произвольной точки M(x, y, z) искомой плоскости вектора PM = {x+1, y-2, z-1}, PQ = {4, -6, 1} и n = {2, 4, -3} также лежат в этой плоскости, и их смешанное произведение равно 0:
откуда получаем искомое уравнение плоскости - x+y+2z-3=0.
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