Question

The equation of the plane passing through the points (1,-1,2) and (2, -2 2) and which is perpendicular to the plane 6x -2y +2z =9 is

• A. $x+y-2z+4=0$
• B. $x-y-2z=4$
• C. $x-2y+z-4=0$
• D. $x+2y-z+4=0$

Answer 1

The correct option is A

$x+y-2z+4=0$

The equation of any plane through (1,-1,2) is a(x-1) + b(y+1) + c(z-2) =0
If it passes through (2,-2,2), then a(2-1) + b(-2+1) + c(2-2) =0
$\Rightarrow a-b+0c=0$
Since the plane is perpendicular to 6x-2y+2z =9, we have
$6a-2b+2c=0$
Solving the equations,
$\frac{a}{-2}=\frac{b}{-2}=\frac{c}{4}=k,say\Rightarrow -2k(x-1)-2k(y+1)+4k(z-2)=0\Rightarrow -2x+2-2y-2+4z-8=0\Rightarrow 2x+2y-4z+8=0\Rightarrow x+y-2z+4=0$