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)`.

Options

A. `7x+5y-4z-8=0`
B. `7x-5y+4z-8=0`
C. `5x-7y+4z-8=0`
D. `5x+7y-4z+8=0`

Answer

B

Explanation

Let the required equation of the plane be
`(3x-y+2z-4)+ lambda(x+y+z-2)=0`
`rArr (3+lambda)x+(lambda-1)y+(2+lambda)z-(4+2lambda)=0`………….(ii)
Since it passes through the point A(2,2,1), we have
`(3+lambda) xx 2+(lambda+1) xx 2 +(2+lambda) xx 1(4 -4/3)=0`.
`rArr (7x)/3-(5y)/3+(4z)/3-8/3=0 rArr 7x-5y+4z-8=0`.