 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/20/d/solution

\nabla \times G = (2 y - 2 z, 2 z - 2 x, 2 x - 2 y) .

It is nonzero, for example

(0, - 2, 2)

(1, 0, 0)

. A differentiable scalar potential would have zero curl of its gradient, so $G$ is not conservative. The fact that its curl vanishes on the line

x = y = z

does not make it vanish throughout the domain.

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