Question

Point $(2,3,-5)$, plane $x+2y-2z=9$

Answer 1

We know that the distance between a point $p(x_1,y_1,z_1)$ and a plane $Ax+By+Cz=D$ is given by,
$d=\left|\frac{A{x}_1+B{y}_1+C{z}_1-D}{\sqrt{A^2+B^2+C^2}}\right|....\left(1\right)$
Thus distance of point $(2,3,-5)$ from the plane $x+2y-2z=9$ is
$d=\left|\frac{2+2\times 3-2(-5)-9}{\sqrt{{\left(1\right)}^2+{\left(2\right)}^2+{(-2)}^2}}\right|=\frac{9}{3}=3$