Question: 77. Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set v=ax (bxc), w (a c)b (a

77. Let a, b, c be nonzero vectors. Assume that b and

77. Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set v=ax (bxc), w (a c)b (a b)c a. Prove that: i. v lies in the plane spanned by b and c. ii. v is orthogonal to a. b. Prove that w also satisfies (i) and (ii). Conclude that v and w are parallel. c. Show algebraically that vw (Figure 23).

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