Q: The equation of planes bisecting the angle between the planes 2x – y + 2z + 3 = 0 and 3x – 2y + 6z + 8 = 0 is / are

(A) 5x – y – 4z – 45 = 0

(B) 5x – y – 4z – 3 = 0

(C) 23x – 13y + 32z + 45 = 0

(D) 23x – 13y + 32z + 5 = 0

Sol. Equation of planes bisecting the angle between given planes are

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

⇒ 5x – y – 4z – 3 = 0 and 23x – 13y + 32z + 45 = 0 are required planes.

Hence (B) and (C) are the correct answers.