Question 13
Given a finite set $X$ of points in the plane. $S$ is a set of vectors $AB$ where $(A, B)$ are some pairs of points in $X$. For every point $A$ the number of vectors $AB$ (starting at $A$) in $S$ equals the number of vectors $CA$ (ending at $A$) in $S$. Show that the sum of the vectors in $S$ is zero.