Question

The equation of the plane which bisects the angle between the planes $3 x - 6 y + 2 z + 5 = 0$ and $4 x - 12 y + 3 z - 3 = 0$ which contains the origin is

• A. $33 x - 13 y + 32 z + 45 = 0$
• B. $x - 3 y + z - 5 = 0$
• C. $33 x + 13 y + 32 z + 45 = 0$
• D. None of these

Answer 1

Answer: (A)

$33 x - 13 y + 32 z + 45 = 0$

Answer 2

Equation of plane bisecting the angle containing origin is (making constant term of same sign)

$\frac { - 3 x + 6 y - 2 z - 5 } { \sqrt { 3 ^ { 2 } + 6 ^ { 2 } + 2 ^ { 2 } } } = + \left[ \frac { 4 x - 12 y + 3 z - 3 } { \sqrt { 4 ^ { 2 } + 12 ^ { 2 } + 3 ^ { 2 } } } \right]$

or $\frac { - 3 x + 6 y - 2 z - 5 } { 7 } = \frac { 4 x - 12 y + 3 z - 3 } { 13 }$

or $67 x - 162 y + 47 z + 44 = 0$.