Уравнение плоскости.
Плоскость задается точкой и двумя векторами. Точку берем М1. Вектор - вектор нормали данной плоскости (1,1,1) и вектор М1М2 М1М2 = (10-5, -9 -(-4), -12 -(-6)) = (5, -5, -6) Строим плоскость
![det \left[\begin{array}{ccc}x-5&y+4&z+6\\1&1&1\\5&-5&-6\end{array}\right] = \\ = -6(x-5)-5(z+6)+5(y+4) -5(z+6)+5(x-5) +6(y+4) = \\ = -x+5-10z-60+11y+44 = 0
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x-11y+10z+11 = 0](https://tex.z-dn.net/?f=+det+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-5%26y%2B4%26z%2B6%5C%5C1%261%261%5C%5C5%26-5%26-6%5Cend%7Barray%7D%5Cright%5D++%3D+%5C%5C+%3D+-6%28x-5%29-5%28z%2B6%29%2B5%28y%2B4%29+-5%28z%2B6%29%2B5%28x-5%29+%2B6%28y%2B4%29+%3D+%5C%5C+%3D+-x%2B5-10z-60%2B11y%2B44+%3D+0%0A%5C%5C+%5C%5C+%0Ax-11y%2B10z%2B11+%3D+0 "det \left[\begin{array}{ccc}x-5&y+4&z+6\\1&1&1\\5&-5&-6\end{array}\right] = \\ = -6(x-5)-5(z+6)+5(y+4) -5(z+6)+5(x-5) +6(y+4) = \\ = -x+5-10z-60+11y+44 = 0
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x-11y+10z+11 = 0")