 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/6/a/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

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

Subtracting cancels the common term, yielding

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

It is generally nonzero: the cross product does not satisfy the associative property.

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