Solution: 7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2, v39, and
Chapter 11, Problem 80(choose chapter or problem)
7680. Properties of dot products Let u = 8u1, u2, u39 , v = 8v1, v2, v39, and w = 8w1, w2, w39. Prove the following vector properties, where c is a scalar. Distributive properties a. Show that 1u + v2 ~ 1u + v2 = _ u _2 + 2 u ~ v + _ v _2. b. Show that 1u + v2 ~ 1u + v2 = _ u _2 + _ v _2 if u is orthogonal to v. c. Show that 1u + v2 ~ 1u - v2 = _ u _2 - _ v _2. 8
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