Question

If the planes $x-3y+4z-1=0$ and $kx-4y+3z-5=0$ are perpendicular, then the value of $k$ is:

• A. $24$
• B. $-24$
• C. $12$
• D. $0$

Answer 1

The correct option is B $-24$

Given two planes are perpendicular if the angle between their normals is ${90}^{\circ }$
The $D.R^{\prime }s$ of the normals are $(1,-3,4)$ and $(k,-4,3)$
$\therefore 1\cdot k-3(-4)+3\cdot 4=0\Rightarrow k=-24$