If the distance between the planes and can be expressed in the form

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

If the distance between the planes

8x + 12y - 14z = 2

and

4x + 6y - 7z = 2

can be expressed in the form

\frac{1}{\sqrt{N}}

, where

N

is natural, then the value of

\frac{N(N+1)}{2}

is (1) 4950 (2) 5050 (3) 5150 (4) 5151