 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-2/5/b/solution

\nabla \times v = (\partial_{y} (3 y^{2} z^{2}) - \partial_{z} (e^{x} + 2 y z^{3}), \partial_{z} (e^{x} y) - \partial_{x} (3 y^{2} z^{2}), \partial_{x} (e^{x} + 2 y z^{3}) - \partial_{y} (e^{x} y)) .

The three components are

6 y z^{2} - 6 y z^{2}

0 - 0

, and

e^{x} - e^{x}

. Consequently

\nabla \times v = (0, 0, 0) .

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