 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-1/5c/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

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

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

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