Question

Find the vector equation of the plane passing through the intersection of the planes and through the point (2, 1, 3)

Answer 1

The equations of the planes are

The equation of any plane through the intersection of the planes given in equations (1) and (2) is given by,

, where

The plane passes through the point (2, 1, 3). Therefore, its position vector is given by,

Substituting in equation (3), we obtain

Substituting in equation (3), we obtain

This is the vector equation of the required plane.