Question

The equation of a plane bisecting the angle between the plane $2x-y+2z+3=0$ and $3x-2y+6z+8=0$ is

• A. $5x-y-4z-45=0$
• B. $5x-y-4z-3=0$
• C. $23x-13y+32z+45=0$
• D. $23x-13y+32z+5=0$

Answer 1

Answer: (B), (C)

The correct options are
B $5x-y-4z-3=0$
C $23x-13y+32z+45=0$

Given planes

$2x-y+2z+3=0,3x-2y+6z+8=0$ for any set of planes, plane bisecting the two planes is obtained by

$\frac{{\Pi }_1}{\left|{\Pi }_1\right|}=\pm \frac{{\Pi }_2}{\left|{\Pi }_2\right|}$

By substituting

$\frac{2x-y+2z+3}{\sqrt{4+1+2^2}}=\pm \frac{3x-2y+6z+8}{\sqrt{9+2^2+36}}\frac{2x-y+2z+3}{3}=\pm \frac{3x-2y+6z+8}{7}$

First Case:

$7(2x-y+2z+3)=3(3x-2y+6z+8)$

On solving: $5x-y-4z-3=0$

Second Case:

$7(2x-y+2z+3)=-3(3x-2y+6z+8)$

We get: $23x-13y+32z+45=0$