(a) Give examples of vectors a, b, c in R3 that show that, in general, it is not true that a × (b × c) = (a × b) × c. (That is, the cross product is not associative.)
(b) Use the Jacobi identity (see Exercise 30 of §1.4) to show that, for any vectors a, b, c in R3,
a × (b × c) = (a × b) × c
if and only if
(c × a) × b = 0.
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