How is it that position is a vector, when a vector needs a direction?

If a particle has a certain position, it is not moving, and hence cannot have a direction. So how can it have a vector? Does the vector direction refer to the direction it would move if it WE'RE moving?|||In order to understand a position vector, first understand a displacement vector.





Displacement is the math/science term for a distance with a direction. Distance is to displacement as speed is to velocity. The first of each pair are scalars, the second are vectors. The idea of a displacement is it completely tells you how to get from point a to point b. For example, the displacement from (3, 2) to (1, -3) is [-2, -5], or it can also be described as having magnitude 5.4 and direction 248 degrees.





Now a position vector is just a displacement vector that assumes point a is the origin, (0, 0). The componentwise representation of the vector will have the same values as the coordinate pair for the position it represents. The magnitude and direction aren't very interesting, but representing a position as a vector allows you to mix it with other vectors where the magnitude and direction are interesting. For example you can add a displacement vector to a position vector to get another position vector.|||Vectors can refer to a bunch of different physical quantities, such as position, velocity, and acceleration. All vectors are is just a magnitude with a direction. The reason why position vectors exist (and why they're necessarily vectors) is that every point in space, relative to an origin point, has a direction and a magnitude. Even when we use an ordered pair like (1, 2), we're using vectors! It just means 1 unit along the x-axis added to 2 units along the y-axis.


Note that this has nothing to do with the actual velocity of the particle at that given time. The velocity is constant and independent of the particle's instantaneous position if there are no external forces acting on it.|||If a particle has xyz coordinates (4,3,-5) for example, it's position vector is the the displacement which would move it from the origin to the position (4,3,-5).





A 'position-vector' is not a true vector, but is very similar and can be treated mathematically as a vector for most purposes.





It is not a true vector because one end has to be the origin. A true vector isn't tied to particular location; it can be 'moved around' (providing its magnitude and direction are not changed) and still be the same vector. This is not true of a position-vector.|||No apostrophe in were. If an apostrophe is placed there, it reads "WE ARE".??


What you are asking is rather like "at x instant in time, how fast is object Y travelling?", which is 0, because in an INSTANT no movement can possibly occur. But people still expect a speed be given!


You particle has a direction from the origin relative to vectors, usually termed X and Y for 2 planes.Your particle does not have to be moving. It is still in that relative position.|||Position is a location in space-time. It has both magnatude and direction in a coordinate system





5 is not a position





(5,3,2, 11:45 Z) is|||If it's a position it's with respect to some point (like the origin) so give it a distance and you just have a position somewhere on the surface of a sphere, give it direction and you hve a point.