 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/1/a/solution

Expanding the cross product componentwise gives

(1, 2, 3)^{T} \times (3, 2, 1)^{T} = (2 - 6, 9 - 1, 2 - 6)^{T} = (- 4, 8, - 4)^{T} .

Its dot product with each original vector is zero, as required.

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