 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/6/b/solution

Each Cartesian component of

a r

contributes

a

to the divergence, while the constant vector contributes zero. Hence

\nabla \cdot (a r - b) = 3 a .

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