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

Let a, b, c be nonzero vectors. Assume that b and c are not parallel, and set

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.

ax(bxc) bxc b a C

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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