 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-1/6c/c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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.

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