Origin of vectors Background 
I was reviewing notes of physics, and i realized that something about the mathematics of vectors was wrong in my head.
Example-problem 
Suppose a vector is $A=5\textbf{i} + 3\textbf{j}$, and other $B=7\textbf{i}+3\textbf{j}$. Then $A-B=C=-2\textbf{i}$.
The question is: Why C is not placed at the origin, from $x=0$ to $x=-2$? Is not it what $C=-2\textbf{i}$ indicates? 
The general question is: does a vector have an origin?

A vector can be placed anywhere, or rather, it does not have location.
