I'm very confused because I don't know how I can prove that the sum of the medians of a triangle is equal to the vector zero. Can someone give me a tip or something? Thanks! (And sorry if this question is too easy for you, guys.)
Say that the triangle is $ABC$. The vector giving the median from $A$ to $BC$ is $(AC+AB)/2$. Similarly, the one from $B$ to $AC$ is $(BA+BC)/2$, and the one from $C$ to $BA$ is $(CB+CA)/2$. Adding these, we get zero since $CB=-BC$, etc.