Question

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).

Answer 1

The equation of any plane through the intersection of the planes, 3x − y + 2z ­− 4 = 0 and x + y + z − 2 = 0, is

`3x − y + 2z ­− 4 + alpha`(x + y + z − 2) = 0 where `alpha in R` ....(1)

The plane passes through the point (2, 2, 1). Therefore, this point will satisfy equation (1).

This is the required equation of the plane.