A equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit distance from the or…

Question

A equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is :

Accepted Answer

Given equation of a plane is

$x - 2y + 2z - 5 = 0$

So, Equation of parallel plane is given by

$x - 2y + 2z + d = 0$

Now, it is given that distance from origin to the parallel planes is $1.$

$$\therefore$$ $$\left| {{d \over {\sqrt {{1^2} + {2^2} + {2^3}} }}} \right| = 1 \Rightarrow d =  \pm 3$$

So equation of required plane

$$x - 2y + 2z \pm 3 = 0$$

Solutions · 1