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moonkey
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Homework Statement
Let C be a simple closed plane curve in space. Let n = ai+bj+ck be a unit vector normal to the plane of C and let the direction on C match that of n. Prove that
(1/2)∫[(bz-cy)dx+(cx-az)dy+(ay-bx)dz]
equals the plane area enclosed by C.
What does the integral reduce to when C is in the xy-plane?
Homework Equations
Stoke's Theorem
∫F.ds=∫(∇×F).dS
The Attempt at a Solution
I really have no idea where to start. Any help would be much appreciated.