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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.