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Stoke's thrm

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



Let [tex] \vec{F} = (z - y)\vec{i} + (x - z)\vec{j} + (y - x)\vec{k} [/tex] . 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.

[tex] \int\limits_C \vec{F} d\vec{r} [/tex] ?

Homework Equations





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:

Answers and Replies

  • #2
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anyone??
 
  • #3
dx
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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
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yes, sorry.. I've edited it now
 
  • #5
dx
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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
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you mean [tex] \int\limits_C \vec{F} d\vec{r} = 20 [/tex] ?
 
  • #7
dx
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CFdr = 2 x (area of rectangle) = 2 x 10 = 20.
 
  • #8
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hmm.. the answer is wrong for some reason
 
  • #9
dx
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Oops, sorry. The magnitude of the curl is √(2² + 2² + 2²) = √12. So the circulation is (√12)(10).
 

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