Q63 / 120 · VITEEE 2019 · Mathematics

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
    $33 x+13 y+32 z+45=0$
  • Correct answer
    D
    None of these

Solution

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

Hence, the correct answer is option: 'D'.

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