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

3 x - 4 y + 2 z - 20 = 0

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2 x - z - 7 = 0

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x - 2 y + z = 11

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10 x - y - 4 z = 27

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Solution

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

$P_{1} : x + 2 y + 2 z = 1 P_{2} : x - 2 y + 2 z = 4$
Let $l_{1} m_{1} n_{1}$ be directions of the plane perpendicular.
$∴ l + 2 m + 2 n = 0 l - 2 m + 2 n = 0 \frac{l}{8} = \frac{m}{0} = \frac{n}{- 4} (l, m, n) = (2, 0, - 1) 2 (x - 2) + 0 (y - 5) + (- 1) (z + 3) = 0 2 x - 4 - z - 3 = 0 2 x - z - 7 = 0$

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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

The correct option is C 2x−z−7=0P1:x+2y+2z=1P2:x−2y+2z=4Let l1m1n1 be directions of the plane perpendicular.∴l+2m+2n=0l−2m+2n=0l8=m0=n−4(l,m,n)=(2,0,−1)2(x−2)+0(y−5)+(−1)(z+3)=02x−4−z−3=02x−z−7=0

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