Let  $P=(-1,0), Q(0,0)$  and  $R(3,3\sqrt{3})$ be three points. Then the equation of the bisector of angle PQR is-------

The line segment QR marks an angle ${60}^{\circ }$ with the positive direction of X- axis
So, the bisector of the angle PQR will make an angle of  ${60}^{\circ }$. With the negative direction of X-axis
Therefore angle of inclination of  ${120}^{\circ }$ and its equation is $y-0=\tan {120}^{\circ }(x-0)$

$$\begin{gathered} y=-\sqrt{3}x \\ y+\sqrt{3}x=0 \end{gathered}$$