It's consistent define position of a particle in some frame as a vector or is just a Physics informality? Velocity and Acceleration can be added up and bring multiplied by real numbers an have physical meaning ( they live in tangent spaces). But what's the physical meaning of adding a position to another, or in relativity's domain, adding two events have some sense? If this have no sense, so define position of a particle as a " vector living in a vector space" is wrong?

Is it consistent to define the position of a particle in some frame as a vector or is just an informal representation? Velocity and acceleration can be added up and multiplied by real numbers and still have physical meaning (they live in tangent spaces). But what is the physical meaning of adding a position to another or, in relativity's domain, does adding two events have any sense? If this has no sense, then defining the position of a particle as a "vector living in a vector space" is surely wrong?