Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set v = a (b
Chapter 12, Problem 73(choose chapter or problem)
Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set v = a (b c), 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 v = w (Figure 24).
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