 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/5a/a/iii/solution

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

In components, part (i) gives

[a \times (b \times c)]_{i} = ϵ_{ijk} a_{j} ϵ_{k l m} b_{l} c_{m} = (δ_{i l} δ_{jm} - δ_{im} δ_{j l}) a_{j} b_{l} c_{m} = b_{i} (a \cdot c) - c_{i} (a \cdot b) .

a \times (b \times c) = b (a \cdot c) - c (a \cdot b) .

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