Для составления уравнения плоскости используем формулу:
x - xA y - yA z - zA
xB - xA yB - yA zB - zA
xC - xA yC - yA zC - zA
= 0
Подставим данные и упростим выражение:
x - 1 y - (-1) z - 2
2 - 1 1 - (-1) 2 - 2
1 - 1 1 - (-1) 4 - 2
= 0
x - 1 y - (-1) z - 2
1 2 0
0 2 2
= 0
(x - 1) (2·2-0·2) - (y - (-1)) (1·2-0·0) + (z - 2) (1·2-2·0) = 0
4 (x - 1) + (-2) (y - (-)) + 2 (z - 2) = 0
4x - 2y + 2z - 10 = 0 или, сократив на 2:
2x - y + z - 5 = 0.
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