Question

An equation of a plane parallel to the plane \(x-2y+2z-5=0\) and at a unit distance from the origin is?

Answer 1

The correct answer is \(x-2y+2z-3=0.\) A plane parallel to \(x−2y+2z−5=0\) can be represented as \(x−2y+2z+k=0\) (Equation i). The perpendicular distance from the origin O(0,0,0) to Equation (i) is 1. Applying the distance formula: \(\frac{|k|}{\sqrt{1+4+4}}=1\), which simplifies to \(|k|=3\). Therefore, \(k=+3\) or \(k=-3\). The equation of the plane is \(x−2y+2z−3=0\).