In: Math
Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines.
L1: x=1-t, y=-2-2t, z=1-t
L2: x=-1+2s, y=-5+4s, z=1+2s
L3: x=-1+2r, y=-5+3r, z=2-r
Find for L1 and L2, L2 and L3, L1 and L3.