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Equation of the plane passing through (-...

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

A

`5x+3y+2z=0`

B

`5x-3y+2z=0`

C

`5x-3y-2z=0`

D

`5x+3y-2z=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Any plane passing through (-2,2,2) is
`a(x+2)+b(y-2)+c(z-2)=0`
`because` It passes through (2,-2,-2).
`rArr" "4a-4b-4c=0` . . .(i)
It is perpendicular to `9x-13y-3z=0`
`:." "9a-13b-3c=0` . . . (ii)
On solving Eqs. (i) and (ii), we get
`(a)/(12-52)=(b)/(-36+12)=(c)/(-52+36)`
`rArr" "(a)/(-40)=(b)/(-24)=(c)/(-16)`
`:.` Required equation of plane is
`-40(x+2)-24(y-2)-16(z-2)=0`
`rArr" "-40x-80-24y+48-16z+32=0`
`rArr" "40x+24y+16z=0`
`rArr" "5x+3y+2z=0`
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