If the plane `x + y +z=1` is rotated through `90^@` about its line of intersection with the plane `x - 2y + 3z=0,` the new position of the plane is

Options

A. `x-5y+4z=1`
B. `x-5y+4z=-1`
C. `x-8y+7z=2`
D. `x-8y+7z=-2`

Answer

D

Explanation

The new position of plane is
`x-2y+3z+lamda(x+y+z-1)=0`
`rArr" "(1+lamda)x+(lamda-2)y+(lamda+3)z-lamda=0`
Since, it is perpendicular to `x+y+z-1=0`
`:." "1(1+lamda)+(lamda-2)+(lamda+3)=0`
`rArr" "lamda=-(2)/(3)`
Hence,required plane is `x-8y+7z=-2`.