 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/16/a/iii/solution

b (a \cdot r) - r (a \cdot b)

. Its first term has divergence

b \cdot \nabla (a \cdot r) = a \cdot b

, while the second contributes

3 a \cdot b

. Therefore

\nabla \cdot [a \times (b \times r)] = - 2 a \cdot b .

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