Two lines are skew if they are neither parallel nor intersecting. For lines r = a_{1} + lambdab_{1} and r = a_{2} + mub_{2}, the shortest distance is: SD = |(a_{2} - a_{1}) . (b_{1} x b_{2})| / |b_{1} x b_{2}|. If b_{1} x b_{2} = 0 (parallel lines), use: SD = |(a_{2} - a_{1}) x b_{1}| / |b_{1}|. If SD = 0 and lines are not parallel, they intersect. The common perpendicular direction is b_{1} x b_{2}.