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

Let the required equation be (3x - y + 2z 4) + `lambda` (x + y + z) = 0
Since it passes through (2, 2, 1) (6 - 2 + 2 - 4) + `lambda` (2 + 2 + 1 2) = 0
2 + 3`lambda` = 0 i.e., `lambda = -(2)/3`
`therefore` The equation of the plane is (3x y + 2z - 4) `-(2)/3`(x + y + z - 2) = 0 i.e., 7x - 5y + 4z - 8 = 0