Question

Equation of a plane bisecting the angle between the planes 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

The correct option is B 5x - y - 4z - 3 = 0

$\frac{2x-y+2z+3}{\sqrt{2^2+(-1{)}^2+2^2}}=\pm \frac{3x-2y+6z+8}{\sqrt{3^2+(-2{)}^2+6^2}}$
$\Rightarrow 7(2x-y+2z+3)=\pm 3(3x-2y+6z+8)$
taking the + ve sign, and $23x-13y+32z+45=0$ taking the – ve sign.
$\Rightarrow 5x-y-4z-3=0$