Two lines r = a_{1} + lambdab_{1} and r = a_{2} + mub_{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.