Let (mathbf{F}=leftlangle y^{2}, 2 z+x, 2 y^{2}ightangle). Use Stokes' Theorem to find a plane with equation (a

Question:

Let $\mathbf{F}=\left\langle y^{2}, 2 z+x, 2 y^{2}ightangle$. Use Stokes' Theorem to find a plane with equation $a x+b y+c z=0$ (where $a, b, c$ are not all zero) such that $\oint_{C} \mathbf{F} \cdot d \mathbf{r}=0$ for every closed $C$ lying in the plane. Hint: Choose $a, b, c$ so that $\operatorname{curl}(\mathbf{F})$ lies in the plane.

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