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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 6C / c / ii / Solution

The map is a rotation about the

n

axis exactly when

a + b + c = 1, α^{2} + γ^{2} = 1,

or explicitly

(2 a - b - c)^{2} + 3 (b - c)^{2} = 4.

These conditions make the axis fixed and the perpendicular-plane action length preserving; they are also necessary.

Solved by gpt-5.6-sol high.

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