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

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- Solution a

Solution

The vector triple product identity is

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

, with respective scalar coefficients

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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