Question

Find the planes bisecting the angle between the planes x + 2y + 2z = 9
and 4x – 3y + 12z + 13 = 0.

• A. 25x+17y+62z-78=0
• B. 25x+17y+62z+78=0
• C. x+35y-10z+156=0
• D. x+35y-10z-156=0

Answer 1

Answer: (A), (D)

The correct options are
A 25x+17y+62z-78=0
D x+35y-10z-156=0

The Equations of the given planes can be written as

– x – 2y – 2z + 9 = 0 and 4x – 3y + 12z + 13 = 0

The bisecting planes are

$\frac{-x-2y-2z+9}{\sqrt{9}}=\pm \frac{4x-3y+12z+13}{\sqrt{169}}$

⇒ – 13x – 26y – 26z + 117 = ± (12x – 9y + 36z + 39)

So 25x + 17y + 62z – 78 = 0 and x + 35y – 10z – 156 = 0 are the bisecting planes.