 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2021-resit/4/a/solution

The parallelepiped volume is the absolute value of the scalar triple product of its edge vectors, equivalently the absolute determinant of the matrix with those columns. Expansion along the first row gives

det A = 1 (1 - 2) - 2 (- 2 - 3) + 2 (4 + 3) = 23.

Therefore

V = ∣ det A ∣ = 23.

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