Question

The equation of the plane passing through the points (1,-3,-2) and perpendicular to planes x +2y+2z=5 and 3x+3y+2z=8, is

• A. 2x -4y +3z-8 =0
• B. 2x-4y-3z+8 =0
• C. 2x+4y+3z+8 =0
• D. x-3y+z-5=0

Answer 1

The correct option is A 2x -4y +3z-8 =0

l+2m+2n=0, 3l+3m+2n=0, $l^2+m^2+n^2=1$, we get l, m, n from these equations and then putting the values in l(x-1)+m(y+3) +n(z+2)=0, we get the required result.
Trick: Checking conversely,
2(x)-4(y)+3(z)-8 =0,
So, it passes through given point.
1(2)+2(-4)+2(3) =0,
So, it is perpendicular to x+2y+2z=5.
3(2)+3(-4)+2(3)=0,
So, it is perpendicular to 3x+3y +2z=8.