Question

Equation of the plane passing through the points $(2,2,1)$ and $(9,3,6)$, and perpendicular to the plane $2x+6y+6z-1=0$ is-

• A. $3x+4y+5z=9$
• B. $3x+4y-5z=9$
• C. $3x-4y+5z=9$
• D. None of the above.

Answer 1

The correct option is B $3x+4y-5z=9$

Equation of plane passes through $(2,2,1)$ is given by,
$a(x-2)+b(y-2)+c(z-1)=\mathrm{0.......}\left(A\right)$
Given it also passes through $(9,3,6)$
$\Rightarrow 7a+b+5c=0......\left(1\right)$
and this plane is perpendicular to plane $2x+6y+6z-1=0$
$\Rightarrow 2a+6a+6c=0.....\left(2\right)$
Solving (1) and (2), we get $a=\frac{-3a}{5},b=\frac{-4a}{5}$
Putting these values in (A) our required plane is,
$3x+4y-5z=9$