 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-2/section-b/6/a/solution

Taking the curl component by component gives

\nabla \times F = (\partial_{y} x - \partial_{z} (x^{2} + 2 y), \partial_{z} (2 x y + z) - \partial_{x} x, \partial_{x} (x^{2} + 2 y) - \partial_{y} (2 x y + z)) = 0 .

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