# Two vector operations and simple expressions

• JiWang
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.

#### JiWang

Thread moved from the technical forums to the schoolwork forums
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?

BvU said:
Hello @JiWang ,

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.

BvU
Last edited:
BvU
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 $$(\partial_j u_l) (\partial_l s_k) = \partial_j ( u_l \partial_l s_k) - u_l \partial_j \partial_l s_k.$$ Then you can write your expression as $$\mathbf{p} = \nabla \times (\mathbf{u} \cdot \nabla \mathbf{s}) - \mathbf{u} \cdot \nabla ( \nabla \times \mathbf{s}).$$

JiWang
Can you expand them to single operations? Thanks.

JiWang said:
Can you expand them to single operations? Thanks.
See the homework guidelines. @pasmith has already done more than enough of your homework!