Для составления уравнения плоскости используем формулу:
<span><span>x - xA </span><span>y - yA </span><span>z - zA</span></span>
<span><span>xB - xA </span><span>yB - yA </span><span>zB - zA</span></span>
<span><span>xC - xA </span><span>yC - yA </span><span>zC - zA</span></span> = 0
Подставим данные и упростим выражение:
<span><span>x - (-1) </span><span>y - 4 </span><span>z - 3</span></span>
<span>3 - (-1) 6 - 4 2 - 3</span>
<span>2 - (-1) (-5) - 4 (-3) - 3</span> = 0
<span><span>x - (-1) </span><span><span>y - </span>4 </span><span><span>z - </span>3</span></span>
<span> 4 2 -1</span>
<span> 3 -9 -6</span> = 0
<span>(x - (-1))*(</span>2·(-6)-(-1)·(-9))<span> - (</span><span><span>y - </span>4)*(</span>4·(-6)-(-1)·3)<span> + </span><span><span>(z - </span>3)*(</span>4·(-9)-2·3)<span> = 0</span>
(-21)<span>x - (-1)</span> + 21<span>y - 4</span> + (-42)<span>z - 3</span> = 0
- 21x + 21y - 42z + 21 = 0
x - y + 2z - 1 = 0