 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-1/1/c/solution

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

The two edge vectors based at

A

are

b - a = (- 3, - 1, 3)

and

c - a = (- 3, 2, 2)

(- 8, - 3, - 9)

, with squared Euclidean norm

64 + 9 + 81 = 154

. The triangle occupies half the corresponding parallelogram, so

area = \frac{1}{2} ∣ (b - a) \times (c - a) ∣ = \frac{154}{2} .

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