Two vector operations and simple expressions

In summary: Hello @JiWang ,:welcome: ##\qquad## !Please post the complete problem statement; see https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/Also, I don't see any vectors on the righthand side in pi=εijksklulj##\ ##In summary, my problem is that I need to simplify an expression involving vectors. I was able to do it using the curl operation, but I need to know how to do it in single operations. See the homework guidelines for more information.
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TL;DR Summary: My problems comes to a vector expression which needs to be simplified

I got an expression
piijksk,lul,j
Here s and u are two vectors. What will be the vector expression of this vector p with curl s, curl u, and other operations?
 
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  • #3
BvU said:
Hello @JiWang ,
:welcome: ##\qquad## !​

Please post the complete problem statement; see https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Also, I don't see any vectors on the righthand side in piijksklulj

##\ ##
I thought that too, but on closer inspection there are commas between the subscripts in the OP. Much clearer in LaTeX: ##s_{k,l}=\partial_ls_k## and similarly ##u##. @JiWang, you should also read the LaTeX Guide.
 
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  • #5
JiWang said:
TL;DR Summary: My problems comes to a vector expression which needs to be simplified

I got an expression
piijksk,lul,j
Here s and u are two vectors. What will be the vector expression of this vector p with curl s, curl u, and other operations?

Use [tex]
(\partial_j u_l) (\partial_l s_k) = \partial_j ( u_l \partial_l s_k) - u_l \partial_j \partial_l s_k.[/tex] Then you can write your expression as [tex]
\mathbf{p} = \nabla \times (\mathbf{u} \cdot \nabla \mathbf{s}) - \mathbf{u} \cdot \nabla ( \nabla \times \mathbf{s}).[/tex]
 
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  • #6
Can you expand them to single operations? Thanks.
 
  • #7
JiWang said:
Can you expand them to single operations? Thanks.
See the homework guidelines. @pasmith has already done more than enough of your homework!
 

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