# Vector integration

aj06

## Homework Statement

Prove $$\int\int_{S}r \times dS=0$$
for any closed surface S.

## The Attempt at a Solution

i used divergence theorem but i didn't make it...

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i used divergence theorem but i didn't make it...

Well, how far did you make it with that? Show us what you've got and we'll be better able to help you.

aj06
the value of r= x^2+y^2+z^2

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Gold Member
the value of r= x^2+y^2+z^2

First,

$$r=||\textbf{r}||=\sqrt{x^2+y^2+z^2}\neq x^2+y^2+z^2[/itex]. Second, is this the entirety of your attempt at the problem? What does this have to do with computing the integral [tex]\int\int_{\mathcal{S}}\textbf{r}\times d\textbf{S}$$

??

aj06
i dont know sir...

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Gold Member
Try applying the divergence theorem to the vector field $\textbf{c}\times\textbf{r}$, where $\textbf{c}$ is any constant (position independent) vector.... What does that give you?

aj06
thank you sir...
but can i have the complete solution of it sir..
thank you

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but can i have the complete solution of it sir..

No. We do not provide complete solutions here. It is unethical and it doesn't really help you learn any problem solving skills.

You need to make some effort and show your work in order to receive further help.