(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove:

[tex]\int \hat{t} ds = 0[/tex]

over C, a closed curve; t is the unit vector tangent to C.

2. Relevant equations

stoke's theorem

3. The attempt at a solution

My issue is that normally, stoke's theorem involves a vector function that we dot into the unit vector (t) (resulting in a scalar) and when we use stoke's theorem, we instead curl that vector function, then dot it into n, the surface normal vector.

However, in this situation, there's no dot product, so we're integrating a vector.

My first attempt was to use the diad product, but I feel like I'm being a bit cavalier with it. I'd just like a hint, but not a full solution so that I can think about it more.

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# Stoke's sans dot-product

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