Question

An 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

Answer 1

The correct option is A

x - 2y + 2z - 3 = 0

Equation of plane parallel to x - 2y + 2z - 5 = 0 is x - 2y + 2z + k = 0 ...(1)

$\frac{|k|}{\sqrt{1+4+4}}=1\Rightarrow |k|=3\Rightarrow k=\pm 3\therefore x-2y+2z-3=0$