Question

The distance of the point $(2,1,-1)$ from the plane $x-2y+4z=9$ is $\frac{m}{\sqrt{21}}$ then $m$ is

Answer 1

Given : Point $(2,1,-1)$ and the plane $x-2y+4z=9$
Using distance formula of a point $P(x_1,y_1,z_1)$ to plane $ax+by+cz=d:$
$=\frac{|a{x}_1+b{y}_1+c{z}_1-d|}{\sqrt{a^2+b^2+c^2}}=\frac{|2-2-4-9|}{\sqrt{1+4+16}}=\frac{13}{\sqrt{21}}$
$\Rightarrow m=13$