# Stoke's thrm

1. May 6, 2009

### -EquinoX-

1. The problem statement, all variables and given/known data

Let $$\vec{F} = (z - y)\vec{i} + (x - z)\vec{j} + (y - x)\vec{k}$$ . Let C be the rectangle of width 2 and length 5 centered at (9, 9, 9) on the plane x + y + z = 27, oriented clockwise when viewed from the origin.

$$\int\limits_C \vec{F} d\vec{r}$$ ?
2. Relevant equations

3. The attempt at a solution

I've already computed the curl F and so now I need to solve the dA. What is the dA here?

Last edited: May 7, 2009
2. May 7, 2009

anyone??

3. May 7, 2009

### dx

Do you mean F = (z - y)i + (x - z)j + (y - x)k? Also, please write out the question completely; don't make us guess. You did this in another recent thread too where you left out an important part of the question because you "didn't think it was relevant".

4. May 7, 2009

### -EquinoX-

yes, sorry.. I've edited it now

5. May 7, 2009

### dx

You should get a constant vector of length 2 for the curl. Did you? It is also perpendicular to the rectangle and pointing outwards, so the circulation is just 2(area of rectangle).

6. May 7, 2009

### -EquinoX-

you mean $$\int\limits_C \vec{F} d\vec{r} = 20$$ ?

7. May 7, 2009

### dx

CFdr = 2 x (area of rectangle) = 2 x 10 = 20.

8. May 7, 2009

### -EquinoX-

hmm.. the answer is wrong for some reason

9. May 7, 2009

### dx

Oops, sorry. The magnitude of the curl is √(2² + 2² + 2²) = √12. So the circulation is (√12)(10).