I have a few (possibly very stupid) questions relating to position vectors; more specifically my confusion about them.
Following Halliday and Resnick's text, we define vectors by their magnitude and direction, but not by their 'location' in space. They give as an example the displacement vector, and draw three of the same vector in different locations to emphasize that shifting the vector does not change it.
Then in the next chapter we are introduced to position vectors relative to a given origin, which is a vector extending from the origin to the position of the particle.
How are we to think about position vectors? It seems like location is also important, even though we only defined vectors as having magnitude and direction.
How do we think about the addition of a displacement to a position vector? We define displacement vectors as the difference between two position vectors. Mathematically this is the same as saying that the final position vector is the result of adding the displacement vector to the initial position vector. The vector algebra doesn't care which ones are assigned the label of 'position' or 'displacement'; do we simply agree that when we add a 'displacement' vector to a 'position' vector, we get a 'position' vector?