The equaiton of the plane passing thorugh the intesection of the planes `3x + 2y - z + 1 =0` and `x + y +z - 2 = 0` is

`(3x + 2y -z+1)+ lambda(x+y+z - 2) = 0" ".......(1)`

Now, this plane passes through the point (2,2,1)

`therefore" "[3(2) +2(2) -1+1] + lambda (2+2+1-2) = 0`

`10 + 3lambda = 0`

`therefore" "lambda = (-10)/(3)`

Putting the value of `lambda` in equation (1) , we get

`(3x + 2y -z+1) (10)/(3) (x+y +z -2) = 0`

`rArr" " 9x + 6y - 3z + 3 - 10y - 10z + 20 = 0`

`rArr" "x + 4y + 13z - 23 =0`

Which is the equaiton of required plane.