 Solution

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

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

Eliminate

V

a = \frac{b ^{'} \times c ^{'}}{a ^{'} \cdot ( b ^{'} \times c ^{'} )} .

This formula actually holds without the unit-length assumptions. Under those assumptions it also says

∣ b^{'} \times c^{'} ∣ = 1/∣ V ∣

; normalizing this cross product alone would lose the sign of

V

and could return

- a

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