Question

In following cases, determine the direction cosines of the normal to the plane and the distance from the origin.

x + y + z = 1

Answer 1

x + y + z = 1 … (1)

The direction ratios of normal are 1, 1, and 1.

This equation is of the form lx + my + nz = d, where l, m, n are the direction cosines of normal to the plane and d is the distance of normal from the origin.

Therefore, the direction cosines of the normal are `1/sqrt3, 1/sqrt3 and 1/sqrt3` the distance of normal from the origin is `1/sqrt3` units.