Equation of the plane passing through (-2,2,2) and (2,-2,-2) and perpendicular to the plane 9x-13y-3z=0 is

Options

A. `5x+ 3y+ 2z=0`
B. `5x-3y+2z=0`
C. `5x-3y-2z=0`
D. `5x+3y-2z=0`

Answer

A

Explanation

Any plane passing through `(-2,2,2)` is
A(x+2)+B(y-2)+C(z-2)=0
`:.` It passes through (2,-2,-2)
`implies 4A-4B-4C=0`....(i)
It is parallel to `9x-13y-3z=0`
`9A-13B-3C=0`
Solving Eqs. (i) and (ii),
`(A)/(12-52)=(B)/(-36+12)=(C)/(-52+36)`
`implies(A)/(-40)=(B)/(-24)=(C)/(-16)`
`:.` Required equation of plane is
`-40(x+2)-24(y-2)-16(z-2)=0`
`implies -40x-80-24y+48-16z+32=0`
`implies 40x+24y+16z=0 `
`implies 5x+3y+2z=0`