# Stoke's thrm

## Homework Statement

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.

$$\int\limits_C \vec{F} d\vec{r}$$ ?

## 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?

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anyone??

dx
Homework Helper
Gold Member
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".

yes, sorry.. I've edited it now

dx
Homework Helper
Gold Member
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).

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

dx
Homework Helper
Gold Member
CFdr = 2 x (area of rectangle) = 2 x 10 = 20.

hmm.. the answer is wrong for some reason

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