Problem 1404 (difficulty: 5/10)

Let \(\displaystyle G=\R^3\setminus\{(x,x,x): x\in\R\}\). Find a differentiable vector field \(\displaystyle X:G\to\R^3\) that is irrotational (\(\displaystyle \curl X={\bf{0}}\)) but is not a gradient field.

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