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Angle between Two Planes

The planes ...

Question

The planes $x - 3 y + 4 z - 1 = 0$ and $k x - 4 y + 3 z - 5 = 0$ are perpendicular then value of $k$ is

A

24

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B

- 24

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C

12

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D

0

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Solution

The correct option is B $- 24$
Let direction ratios of the perpendicular to the plane
$x - 3 y + 4 z - 1 = 4$ are $a_{2} = 1, b_{1} = - 3, c_{1} = 4$
and that of planes will be perpendicular if
$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$
$k + (- 3) \times (- 4) + 4 \times 3 = 0$
$k + 12 + 12 = 0$
$k = - 24$

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