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

Question

A equation of a plane parallel to the plane x - 2y + 2z -5 = 0 and at a unit distance from the origin is : (A) x - 2y + 2z - 3 = 0 (B) x - 2y + 2z + 1 = 0 (C) x - 2y + 2z - 1 = 0 (D) x - 2y + 2z + 5 = 0

Tardigrade Admin · 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 plane is 1.

∴ ∣ ∣ \frac{d}{1 ^{2} + 2 ^{2} + 2 ^{2}} ∣ ∣ = 1 \Rightarrow d = \pm 3

So equation of required plane

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

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

x - 2y + 2z - 3 = 0

x - 2y + 2z + 1 = 0

x - 2y + 2z - 1 = 0

x - 2y + 2z + 5 = 0

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 plane is 1. ∴∣∣​12+22+22​d​∣∣​=1⇒d=±3 So equation of required plane x−2y+2z±3=0