 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/6/b/solution

Each component of the cross product in part (a) is independent of the coordinate with respect to which the divergence differentiates it. Thus

\nabla \cdot (F \times G) = \partial_{x} sin (y - z) + \partial_{y} sin (z - x) + \partial_{z} sin (x - y) = 0 .

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