(a) Using vector methods, show that the distance between
Chapter , Problem 25(choose chapter or problem)
(a) Using vector methods, show that the distance between two nonparallel lines l1 and l2 is given by d = |(v2 v1) (a1 a2)| a1 a2 , where v1, v2 are any two points on l1 and l2, respectively, and a1 and a2 are the directions of l1 and l2. [HINT: Consider the plane through l2 that is parallel to l1. Show that the vector (a1 a2)/ a1 a2 is a unit normal for this plane; now project v2 v1 onto this normal direction.] (b) Find the distance between the line l1 determined by the points (1, 1, 1) and (0, 0, 0) and the line l2 determined by the points (0, 2, 0) and (2, 0, 5).
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