I was given this question in class and I assume it is a spin off of Green's theorem for finding the area of a closed curve *λ* in 2D but expanded to 3D I believe. Anyways I am pretty confused about it so if anyone could help I would appreciate it,.
Question: Let *λ* be a simple closed smooth space curve that lies in a plane with unit normal vector n = (a, b, c) and has positive orientation with respect to the normal vector n of the plane. Show that the plane area enclosed by *λ* is 1/2∫*_**λ *(*b**z*−*c**y*)*d**x*+(*c**x*−*a**z*)*d**y*+(*a**y*−*b**x*)*d**z* |