 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/6/solution

Expanding the cross product gives

F \times G = - x z - yz x^{2} + y^{2} .

Taking its divergence component by component,

\nabla \cdot (F \times G) = \partial_{x} (- x z) + \partial_{y} (- yz) + \partial_{z} (x^{2} + y^{2}) = - 2 z .

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