Find the equation of the plane which passes through the point `(2,2,2)` and through the intersection of the planes `3x-y+2z=4` and `x + y+z = 2`.

Explanation

Let the equation of plane through the intersection of given planes be
`(3x-y+2z-4)+lambda(x+y+z-2)=0"……"(1)`
It passes through the point `(2,2,2)`
`:. (6-2+4-4)+lambda(2+2+2-2) = 0`
`rArr lambda = - 1`
`:.` Equation of plane
`(3x-y+2z-4) - (x+y+z-2) = 0`
`rArr 2x+2y +z-2 = 0`