 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/14/a/solution

a \times (b \times c) = b (a \cdot c) - c (a \cdot b) .

Thus the expression lies in the linear span of

b

and

c

a \cdot c

and

- a \cdot b

. The order and the minus sign matter because the cross product is not an associative operation.

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