Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 3 / 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) .

Consequently a choice of the requested coefficients is

α = 0, β = a \cdot c, γ = - a \cdot b .

These are the standard identity's coefficients, even if the particular three vectors are linearly dependent and a representation need not be unique.

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