# Stokes' theorem and unit vector

1. Aug 13, 2009

### Sami Lakka

1. The problem statement, all variables and given/known data
Use Stokes' theorem to show that

$$\oint\ \hat{t}*ds = 0$$

Integration is done closed curve C and $$\hat{t}$$ is a unit tangent vector to the curve C
2. Relevant equations
Stokes' theorem

$$\oint F* \hat{t}*ds = \int\int \hat{n}*curl(F)*ds$$

3. The attempt at a solution

Ok, this is really teasing me because I know that is probably simple. Could someone help please?

2. Aug 13, 2009

### Dick

Your notation is pretty sloppy. If t=(tx,ty,tz) the result of your first integral is the vector whose first coordinate is the integral of tx*ds, second is integral ty*ds, and third integral tz*ds. You want to show all of those are zero. Apply Stokes to the constant vector field F=(1,0,0). What does that tell you? What other vector fields would be good to use?

3. Aug 14, 2009

### Sami Lakka

Yes, sorry about the notation, it is direct copy from the book that I'm studying. t is a unit vector with components (dx/ds, dy/ds, dz/ds) so after the multiplication the integral is taken from vector (dx, dy, dz)

4. Aug 14, 2009

### Sami Lakka

Ok, now I think I got it. I should use Stokes' theorem with F=1 (scalar). What bothered me was that I was all the time looking at the cross product in curl which is not defined for scalars. Of course the cross product is only a notation, not actual vector cross product.

5. Aug 14, 2009

### Dick

No! You can't use Stokes theorem on a scalar. Use it on the vector F=(1,0,0)=1*i+0*j+0*k.