 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/1/a/solution

The prescribed orientation orders the two edges from

A

c - a

followed by

b - a

S = \frac{1}{2} (c - a) \times (b - a) = \frac{1}{2} (- 1, 0, 1)^{T} \times (- 1, 1, 0)^{T} = - \frac{1}{2} (1, 1, 1)^{T} .

The sign agrees with the right-hand rule for the traversal

A \to C \to B \to A

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