Question: (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}) denotes (leftlangleDelta F_{1}, Delta F_{2}, Delta F_{3}ightangle). 0x2

\(\Delta\) denotes the Laplace operator defined by

0x2 ' ' +

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

0x2 ' ' +

Step by Step Solution

3.42 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

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 full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!