Free Vectors can only be added if they are in cartesian coordinates.
A cartesian free Vector can be added with a rooted Vector
Rooted Vectors can be added if they are in the same coordinate system and are rooted at the same point.
When a vector field and a rooted Vector are added, the vector field is evaluated at the root point of the vector and the operation is carried through. The coordinate system of the sum and the vector field are the same.
Vector Fields can be added if they are in the same coordinate system.
Position Vectors can also be added, the result is a position Vector.