In a coordinate system position is just a label for the points, so we can distinguish between different points. Then why we use a position vector to specify the position as it is just a label and nothing else. We can use colours if we want to label the points and it would be fine. For example, Paris is a label for a specific location on earth and it does not have magnitude or direction. Please explain it in as simple terms as you can do not use jargon.
In: Physics
What properties would that “label” have to be useful? Given two positions using these labels, is there a method that allows one to determine properties such as their relative distances or some kind of directional information? Given a label, how could you identify points that are “nearby”? How could you quantify that?
You are not wrong saying you can make up labels as much as you please. How would you actually make them useful?
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