(Delta) denotes the Laplace operator defined by Prove the identity [ operatorname{curl}(operatorname{curl}(mathbf{F}))=abla(operatorname{div}(mathbf{F}))-Delta mathbf{F} ] where (Delta mathbf{F})...

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$\Delta$ denotes the Laplace operator defined by

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Prove the identity
\[
\operatorname{curl}(\operatorname{curl}(\mathbf{F}))=abla(\operatorname{div}(\mathbf{F}))-\Delta \mathbf{F}
\]
where $\Delta \mathbf{F}$ denotes $\left\langle\Delta F_{1}, \Delta F_{2}, \Delta F_{3}ightangle$.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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(Delta) denotes the Laplace operator defined by Prove the identity [ operatorname{curl}(operatorname{curl}(mathbf{F}))=abla(operatorname{div}(mathbf{F}))-Delta mathbf{F} ] where (Delta mathbf{F})...

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Step by Step Answer:

The identity you provided is a wellknown vector calculus identity involving the curl of the curl of a vector field mathbfF This identity is given by a...View the full answer

Calculus

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