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).

Explanation

`(3x - y + 2z -4) + alpha(x + y + z -2 ) = 0` , Where `alpha in R ldots (1)`


If the plane passes through the point `(2,2,1)`. So it should satisfy the equation `(1)`.


`therefore (3*2-2+2*1-4) + alpha(2+2+1-2)=0`

`Rightarrow 2+ 3alpha = 0`

`Rightarrow alpha = -2/3`

Substituting `alpha = -2/3` in equation `(1)`, we obtain

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