Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics IV / 1 / d / iii

Table of contents
- Solution iii

Solution

Apply the squared scalar triple product from cyclic cross products proved in c:

a^{'} \cdot (b^{'} \times c^{'}) = \frac{( b \times c ) \cdot [( c \times a ) \times ( a \times b )]}{V ^{3}} = \frac{V ^{2}}{V ^{3}} .

Hence the reciprocal basis has scalar triple product

a^{'} \cdot (b^{'} \times c^{'}) = 1/ V

, with its sign retained.

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

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