PX275 - D4d - comments

for a closed curve (eg: the circular loop in the $x$ - $y$ plane), the total vector surface area of any surface spanning curve is a property of the curve itself
the shape of the surface is irrelevant
a closed curve and an open surface have been considered

{\vec{S}}_{2, t o p} = - {\vec{S}}_{2, b o t t o m} ⟹ {\vec{S}}_{2} = 0