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Question

The equation of the plane through the point $$(2, 5, -3)$$ perpendicular to the planes $$x+2y+2x=1$$ and $$x-2y+2x=4$$ is


A
3x4y+2z20=0
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B
2xz7=0
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C
x2y+z=11
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D
10xy4z=27
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Solution

The correct option is C
$$2x-z-7=0$$

$${ P }_{ 1 }:x+2y+2z=1\\ { P }_{ 2 }:x-2y+2z=4$$
Let $$ { l }_{ 1 }{ m }_{ 1 }{ n }_{ 1 }$$ be directions of the plane perpendicular.
$$\therefore l+2m+2n=0\\ l-2m+2n=0\\ \cfrac { l }{ 8 } =\cfrac { m }{ 0 } =\cfrac { n }{ -4 } \\ (l,m,n)=(2,0,-1)\\ 2(x-2)+0(y-5)+(-1)(z+3)=0\\ 2x-4-z-3=0\\ 2x-z-7=0$$

Mathematics

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