 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/2/solution

The boundary order fixes the orientation. Two edges issuing from

A

are

A B = (0, 0, 1)

and

A D = (1, 1, 0)

. Their cross product gives the oriented vector area:

A = A B \times A D = - 1 10 .

Its norm is

2

, the ordinary rectangle area. The sign agrees with traversing

A \to B \to C \to D \to A

by the right-hand orientation rule.

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