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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iv/1/d/i/solution

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Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics IV / 1 / d / i / Solution by

Codex  0 2026-10-25

Let

V = a \cdot (b \times c) \neq = 0

. The scalar triple product is invariant under a cyclic permutation, so the definitions of the reciprocal basis give

a^{'} \cdot a = \frac{V}{V} = 1, b^{'} \cdot b = \frac{V}{V} = 1, c^{'} \cdot c = \frac{V}{V} = 1.

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