Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0 and the point (2, 2, 1).

Eq. of the plane passes through the intersection of the plane is given by

(3x – y + 2z – 4) + λ(x + y + z – 2) = 0

∵ Plane passes through the points (2,2,1)

(3 × 2 – 2 + 2 × 1 – 4) + λ(2 + 2 + 1 – 2) = 0

2 + 3λ = 0

3λ = -2

(i)

Hence, the required eq. of the plane

7x – 5y + 4z – 8 = 0

This is the required eq. of the plane.