Evaluate F dr, where F(x, y, z)= xyi +4zj +3yk and C is defined by the intersection of the plane x+z = 5 and the cylinder x2 +y² = 9. C is oriented counterclockwise. Apply Stoke's Theorem. Take S to be the ellipse defined by the intersection of the plane and the cylinder. Evaluate over the region D projected down into the xy-plane: D= {(x, y)|x² + y <9}. G(x, y, z)= z-x-5=0 and find VG.

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