Question

lf the planes $2x+3y-4z+5=0,kx-y+2z+3=0$ are perpendicular, then $k=$

• A. $\frac{11}{3}$
• B. $\frac{11}{2}$
• C. $\frac{-11}{2}$
• D. $\frac{9}{2}$

Answer 1

Answer: (B)

$\frac{11}{2}$

Given equation of planes are $2x+3y-4z+5=0,kx-y+2z+3=0$

If given planes are perpendicular then dot product of their normal vector should be zero.

$\Rightarrow 2\left(k\right)+3(-1)-4\left(2\right)=0$
$\Rightarrow 2k-11=0$

$\Rightarrow k=\frac{11}{2}$