Let F(x,y,z) = (-xy, x, 0) and let C be the curve of intersection of the plane x+y+z=1 and the cylinder x² + y² = 1, oriented counterclockwise when viewed from above. (a) Sketch the surfaces and highlight the curve of intersection C. (b) Parametrize the curve C. (c) Evaluate fF.dr using the definition; that is fF.dr = f F(F(t)) - F'(t)dt.

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