Visualising the Shortest Distance between Skew Lines
In two dimensions, a pair of lines can be any one of either intersecting or parallel. But in three dimensional space there is a third alternative. A pair of lines in 3D can be skew lines. A pair of lines that do not intersect and are not parallel either are characterised as skew lines. And that’s the only way to describe them. Skew lines are straight lines in 3D that are neither pointing in the same two directions nor cutting through each other . We can always find a plane in 3D that contains two intersecting lines. Same is true for a pair of parallel lines as well. But skew lines can never be both in the same plane. But for a given pair of skew lines we can always find a unique pair of parallel planes each containing one of the two lines. This is an important property which helps us derive the formula for finding the shortest distance between two skew lines - a topic studied in 3D geometry. But first, what is the shortest distance between two lines?...