 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/i/solution

The fixed vectors have constant components, so

a \cdot b

is constant,

\nabla \cdot a = 0

and

\nabla \cdot r = 3

. Hence the divergence is

\nabla \cdot [2 (a \cdot b) r + a] = 6 a \cdot b .

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