Browse Questions

# Find the $\perp$ distance of the point (3,-2,1) from the plane $2x-y+2z+3=0$

Toolbox:
• Distance of any point $(x_1,y_1,z_1)$ from the plane $ax+by+cz+d=0$ is given by $\bigg| \large\frac{ax_1+by_1+cz_1+d}{\sqrt{a^2+b^2+c^2}} \bigg|$
Given point $Q(3,-2,1)$ and Eqn. of plane $2x-y+2z+3=0$
We know that the distance of any point $(x_1,y_1,z_1)$ from the plane $ax+by+cz+d=0$ is given by
$\bigg| \large\frac{ax_1+by_1+cz_1+d}{\sqrt{a^2+b^2+c^2}} \bigg|$
$\perp$ distance =$\bigg|\large\frac{6+2+2+3}{\sqrt {2^2+(-1)^2+2^2}}\bigg|=\frac{13}{3}$