Two lines r = $a_{1}$ + lambda**$b_{1}$** and r = $a_{2}$ + mu**$b_{2}$** are coplanar (intersecting or parallel) iff: [$a_{2}$ - $a_{1}$, $b_{1}$, $b_{2}$] = 0. This is equivalent to saying the shortest distance between them is zero. The plane containing both coplanar lines can be found using the normal $b_{1}$ x $b_{2}$ and any point on either line. If lines are parallel ($b_{1}$ x $b_{2}$ = 0), check if any point of one line lies in the plane containing the other.