The two planes x - 2 y + 4 z = 10 and 18 x + 17 y + k z = 50 are perpendicular, if k is equal to:

Question

The two planes $x - 2 y + 4 z = 10$ and $18 x + 17 y + k z = 50$ are perpendicular, if $k$ is equal to:

Smart Achievers · Accepted Answer

(2)

Ans. 4

Explanation:

$\Rightarrow$ $18 \times 1 + 17 \times (- 2) + 4 \times k = 0$

$\Rightarrow$ $18 - 34 + 4 k = 0$ $[using a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0]$

$\Rightarrow$ $4 k = 16 \Rightarrow k = 4$

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