Two lines are skew if they are neither parallel nor intersecting. For lines r = $a_{1}$ + lambda**$b_{1}$** and r = $a_{2}$ + mu**$b_{2}$, 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 $b_{2}$.