Question

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. $5x+3y-2z=0$

Answer 1

The correct option is A $5x+3y+2z=0$

Any plane passing through $(-2,2,2)$ is $A(x+2)+B(y-2)+C(z-2)=0$
$\because$ It passes through $(2,-2,-2)$
$\Rightarrow 4A-4B-4C=0$ $..........\left(i\right)$
It is parallel to $9x-13y-3z=0$
$\therefore 9A-13B-3C=0$ $..........\left(ii\right)$
Solving Eqs.$\left(i\right)$ and $\left(ii\right)$,
$\frac{A}{12-52}=\frac{B}{-36+12}=\frac{C}{-52+36}$
$\Rightarrow \frac{A}{-40}=\frac{B}{-24}=\frac{C}{-16}$
$\therefore$ Required equation of plane is $-40(x+2)-24(y-2)-16(z-2)=0$
$\Rightarrow -40x-80-24y+48-16z+32=0$
$\Rightarrow 40x+24y+16z=0$
$\Rightarrow 5x+3y+2z=0$