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Q.
A equation of a plane parallel to the plane x - 2y + 2z -5 = 0 and at a unit distance from the origin is :
Three Dimensional Geometry
Solution:
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.
$\therefore \, \left|\frac{d}{\sqrt{1^{2} + 2^{2} + 2^{2}}} \right| = 1 \Rightarrow d = \pm3 $
So equation of required plane
$x - 2y +2z \pm3 = 0 $