Question

Find the equation of the plane through the line of intersection of the planes and which is perpendicular to the plane

Answer 1

The equation of the plane through the intersection of the planes, and , is

The direction ratios, a₁, b₁, c₁, of this plane are (2λ + 1), (3λ + 1), and (4λ + 1).

The plane in equation (1) is perpendicular to

Its direction ratios, a₂, b₂, c₂, are 1, −1, and 1.

Since the planes are perpendicular,

Substituting in equation (1), we obtain

This is the required equation of the plane.