Let (mathbf{F}) be a vector field whose curl and divergence at the origin are [ operatorname{curl}(mathbf{F})(0,0,0)=langle 2,-1,4angle,

Question:

Let $\mathbf{F}$ be a vector field whose curl and divergence at the origin are
\[
\operatorname{curl}(\mathbf{F})(0,0,0)=\langle 2,-1,4angle, \quad \operatorname{div}(\mathbf{F})(0,0,0)=-2
\]

Suppose that $\mathbf{v}$ is the velocity field of a fluid and imagine placing a small paddle wheel at the origin. Find the equation of the plane in which the paddle wheel should be placed to make it rotate as quickly as possible.

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