 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1/20/a/iii/solution

Take the curl component by component:

F = (\partial_{y} \frac{y ^{3}}{3} - \partial_{z} \frac{x ^{3}}{3}, \partial_{z} \frac{z ^{3}}{3} - \partial_{x} \frac{y ^{3}}{3}, \partial_{x} \frac{x ^{3}}{3} - \partial_{y} \frac{z ^{3}}{3}) = (y^{2}, z^{2}, x^{2}) .

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