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

(A) 23x – 13y + 32z + 45 = 0

(B) 5x – y – 4z = 3

(C) 5x – y – 4z + 45 = 0

(D) 23x – 13y + 32z + 3 = 0

Sol. a_{1}a_{2} + b_{1} b_{2} + c_{1}c_{2} = 6 + 2 + 12 =positive

So acute angle bisector is $ \large \frac{2x – y + 2z +3}{3} = – \frac{3x-2y + 6z + 8 }{7} $

⇒ 23x – 13y + 32z + 45 = 0

Hence (A) is the correct answer.

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