Question

Find the equation of the plane through the line of intersection of the planes

x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

Answer 1

The equation of the plane through the intersection of the planes, x+y+z =1 and 2x+3y+4z=5 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 x-y+z=0
Its direction ratios, a₂, b₂, c₂, are 1, −1, and 1. Since the planes are perpendicular,