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Angle between Two Planes

The equation ...

Question

The equation of the plane mid-parallel to the planes $2 x - 3 y + 6 z - 7 = 0$ and $2 x - 3 y + 6 z + 7 = 0$ is

A

2 x - 3 y + 6 z = 0

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B

2 x - 3 y + 6 z = 8

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C

2 x - 3 y - 6 z = 0

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D

2 x - 3 y + 6 z = 14

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Solution

The correct option is A $2 x - 3 y + 6 z = 0$
The required plane is parallel to the given planes and lies mid-way between them.
The plane equation mid-way between the planes $a x + b y + c z + d_{1} = 0$ and $a x + b y + c z + d_{2} = 0$ is $a x + b y + c z + \frac{d_{1} + d_{2}}{2} = 0$
$∴$ Required equation of plane is
$2 x - 3 y + 6 z = 0$

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Angle between Two Planes

Standard XII Mathematics

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