 Solution

ID: 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/solution

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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