Let L1 be the line passing through the point P1=(4, 5, −5) with direction vector →d1=[0, −1, 1]T, and let L2 be the line passing through the point P2=(13, 0, 0) with direction vector →d2=[4, −1, 3]T.

Question

Let L1 be the line passing through the point P1=(4, 5, −5) with direction vector →d1=[0, −1, 1]T, and let L2 be the line passing through the point P2=(13, 0, 0) with direction vector →d2=[4, −1, 3]T.
Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d.

Steve · Answer

You can find a helpful discussion here: https://math.stackexchange.com/questions/2168307/distance-between-2-skew-lines-weird-result