Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set
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Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set
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v = ax (bx c), (a) Prove that: (i) v lies in the plane spanned by b and c. (ii) v is orthogonal to a. w = (a c)b (a . b)c . (b) Prove that w also satisfies (i) and (ii). Conclude that v and w are parallel. (e) Show algebraically that v = w (Figure 23).
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a Since v is the cross product of a and another vector b c then v is orthogonal to a Furthermore v i...View the full answer
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