Three Dimensional Geometry

they are parallel when $l a+m b+n c=0$

they are perpendicular when $\frac{1}{a}=\frac{m}{b}=\frac{n}{c}$

the direction ratios of the bisectors of the angles between the two lines are $l \pm a, m \pm b$ and $n \pm c$

the direction ratios of the bisectors of the angles between the two lines are la, $m b$ and $n c$