 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/iv/solution

Again write the field as

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

. The second term has zero curl. Applying the product rule to the first gives

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

. Thus

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

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