If l1, m1, n1 and l2, m2, n2 are the direction cosines of two concurrent lines, then the direction cosines of the lines bisecting the angles between them are proportional to :
1
\(\pm \frac{l_{1}}{l_{2}}, \pm \frac{m_{1}}{m_{2}}, \pm \frac{n_{1}}{n_{2}} \)
2
\(\pm \sqrt{l_{1} l_{2}}, \pm \sqrt{m_{1} m_{2}}, \pm \sqrt{n_{1} n_{2}} \)
3
l1 ± l2, m1 ± m2, n1 ± n2
4
\(\pm \sqrt{\frac{l_{1}}{l_{2}}}, \pm \sqrt{\frac{m_{1}}{m_{2}}}, \pm \sqrt{\frac{n_{1}}{n_{2}}} \)