A vector field (mathbf{F}) is incompressible if (operatorname{div}(mathbf{F})=0) and is irrotational if (operatorname{curl}(mathbf{F})=mathbf{0}). Let (mathbf{F}) be an

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A vector field $\mathbf{F}$ is incompressible if $\operatorname{div}(\mathbf{F})=0$ and is irrotational if $\operatorname{curl}(\mathbf{F})=\mathbf{0}$.

Let $\mathbf{F}$ be an incompressible vector field that is everywhere tangent to level surfaces of $f$. Prove that $f \mathbf{F}$ is incompressible.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 28, 2024 12:00 AM

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A vector field (mathbf{F}) is incompressible if (operatorname{div}(mathbf{F})=0) and is irrotational if (operatorname{curl}(mathbf{F})=mathbf{0}). Let (mathbf{F}) be an

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Calculus

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