 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/14/b/solution

The volume of a parallelepiped is the absolute scalar triple product of its three edge vectors. Since

OP \times OQ = (0, 0, 3)

V = (OP \times OQ) \cdot OR = 3 .

The factor

1/6

appropriate to a tetrahedron must not be applied to this parallelepiped.

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