Question

The perpendicular distance from the origin to the plane $x-2y+2z-9=0$ is

• A. $3$
• B. $6$
• C. $4$
• D. $2$

Answer 1

The correct option is A $3$

Given plane is $x-2y+2z-9=0$

General Case:

Perpendicular distance from point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ is given as

$P=\left|\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}\right|$

Here $(a,b,c)=(1,-2,2)(x_1,y_1,z_1)=(0,0,0)$

Now perpendicular distance

$P=\left|\frac{0+0+0+9}{\sqrt{1+4+4}}\right|P=\frac{9}{3}=3$

Perpendicular distance from origin to given plane is $3$