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Question: The equation of the plane bisecting the acute angle between the planes 2x – y + 2z + 3 = 0 and 3x – ...

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

Answer

23x – 13y + 32z + 45 = 0

Explanation

Solution

a1a1 + b1b2 + c1c2 = 6 + 2 + 12 is positive

so that the acute angle bisector is

2xy+2z+33=3x2y+6z+87\frac { 2 x - y + 2 z + 3 } { 3 } = - \frac { 3 x - 2 y + 6 z + 8 } { 7 }

⇒ 23x − 13y + 32z + 45 = 0