 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2015/7/solution

Subtract the first vertex from the remaining three to obtain edge vectors

a = (1, 2, - 2)

b = (0, 1, 3)

c = (- 1, - 1, 0)

a \cdot (b \times c) = (1, 2, - 2) \cdot (3, - 3, 1) = - 5.

A tetrahedron occupies one sixth of the corresponding parallelepiped, so its volume is

V = \frac{1}{6} ∣ a \cdot (b \times c) ∣ = \frac{5}{6} .

The absolute value removes the orientation sign of the determinant.

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