Let $P \equiv (-3, 0)$,$Q \equiv (0, 0)$,and $R \equiv (3, 3\sqrt{3})$ be three points. Then the equation of the bisector of the angle $\angle PQR$ is

The equation of the bisector of the angle between the lines $x + 2y - 11 = 0$ and $3x - 6y - 5 = 0$ which contains the point $(1, -3)$ is

The straight line $x+y+1=0$ bisects an angle between a pair of lines,of which one is $2x-3y+4=0$. Then the equation of the other line in that pair is

Let $B_1: 3x + 4y - 7 = 0$ and $B_2: 4x - 3y - 14 = 0$ be the angle bisectors of the angle between the lines $L_1 = 0$ and $L_2 = 0$. If $L_1$ passes through the point $(1, 2)$,then which of the following is true?

Let $A, B, C$ be three points in the $xy$-plane,whose position vectors are given by $\sqrt{3} \hat{i} + \hat{j}$,$\hat{i} + \sqrt{3} \hat{j}$,and $a \hat{i} + (1 - a) \hat{j}$ respectively with respect to the origin $O$. If the distance of the point $C$ from the line bisecting the angle between the vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ is $\frac{9}{\sqrt{2}}$,then the sum of all the possible values of $a$ is :

Find the equation of the bisector of the obtuse angle between the lines $3x - 4y + 7 = 0$ and $12x + 5y - 2 = 0$.