 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/a/solution

Since

r \cdot r = x^{2} + y^{2} + z^{2}

, its gradient is

\nabla (r \cdot r) = (2 x, 2 y, 2 z) = 2 r .

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