Find the equations of the planes parallel to the plane x – 2y + 2z – 3 = 0 and which are at a unit distance from the point (1, 1, 1).

Question

Philoid · Accepted Answer

Since the planes are parallel to x – 2y + 2z – 3 = 0, they must be of the form:

x – 2y + 2z + θ = 0

We know, the distance of point (x₁,y₁,z₁) from the plane

is given by:

According to the question, the distance of the planes from (1, 1, 1) is 1 unit.

⟹

⟹ or

⟹ θ = 2 or –4

⟹ The required planes are:

x – 2y + 2z + 2 = 0 and x – 2y + 2z – 4 = 0