Q. The equation of the bisector of the obtuse angle between the lines $3x - 4y + 7 = 0$ and $- 12x - 5y + 2 = 0,$ is
A) $21x + 77y - 101 = 0$
B) $99x - 27y + 81 = 0$
C) $21x - 77y + 101 = 0$
D) None of these
Explanation
(a)
$\because a_{1}a_{2} + b_{1}b_{2} = 3 \times ( - 12) + ( - 4)( - 5) = - 36 + 20 = - 16 \leq 0$
$\therefore\$Obtuse angle bisector is
$\frac{3x - 4y + 7}{\sqrt{3^{2} + ( - 4)^{2}}} = - \frac{- 12x - 5y + 2}{\sqrt{( - 12)^{2} + ( - 5)^{2}}}$
$\Rightarrow 13(3x - 4y + 7) = - 5( - 12x - 5y + 2)$
$\Rightarrow 21x + 77y - 101 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.