Inspired by a question in Griffiths' E&M book (1.10), I am wondering why the components of a vector do not change when the coordinate system is translated by a constant vector. I understand that, for instance, the velocity of something moving in a coordinate system won't change if we then transform to another coordinate frame translated by a constant distance. By certainly the position vector would (e.g., if in the first frame an event is at the origin, the components will not be (0,0,0) in any translated frame). In trying to work out the answer to my question on my own, I'm guessing it has something to do with the fact that translations don't change the BASIS vectors we use to describe the coordinate, whereas rotations or stretches do change the basis vectors? But the example of position as compared to any other vector quantity still confuses me when I think of what would change due to a translation. Thanks!