Origin of vectors with physical meaning I was reviewing notes of physics, and i realized that something about the mathematics of vectors was wrong in my head.
Suppose a vector is $\vec{A}=5\textbf{i} + 3\textbf{j}$, and other $\vec{B}=7\textbf{i}+3\textbf{j}$. Then $\vec{A}-\vec{B}=\vec{C}=-2\textbf{i}$.
Now, take for example a point charge vector field:
$${\mathbf  {E}}({\mathbf  {r}})= \ q_{i}{\frac  {{\mathbf  {r}}-{\mathbf  {r}}_{i}}{|{\mathbf  {r}}-{\mathbf  {r}}_{i}|^{3}}}$$
(Dropped the constants)
This kind of vectors have a new implementation, they are attached to a point in space.
I do not know if it is the same with velocity vector.
I just want to know if the idea is wrong and what should I review.
 A: When you say "they are attached to a point in space" you are implicitly translating the concept of "function" in to "attached". The field is a function that relate a vector with another, in terms of mathematics this two vector are still free vectors like the one you talked before. It is the interpretation, the meaning you give to this vectors that leads to that sort of difference, the first, the domain vectors, are interpreted as position, while the image vector represent forces, so you are binding forces to a position, but the two vectors themselves, taken separately from the relation have nothing different from velocity vectors, it's the relation, the function that creates that "binding", a function is indeed binding couple of elements.
A: In purely mathematical sense, you can put the origin of the electric field vector $\textbf{E}$ everywhere in the space. This is ok, actually.
However, the object which your are considering is not only mathematical but physical: Electric field vector. Remember that electric field is defined as a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge at a point,by an infinitesimal test charge at that point, so each E vector has its defined origin to identify the point which the source act on. That is to say, the origin of the E vector has its own physical meaning. 
