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
One way to describe where Paris is would be to say. It is at 48° 51′ 24″ N, 2° 21′ 6″ E and an elevation of 30 to 130 .
This is a direction from the center of the earth and a distance from it (the distance to what the French have defined as sea-level plus a few more meters.)
You can use shorthands for that like “Paris” or “Lutetia” or “City of Light” or “the capital of France” or even assign it some color or anything else. However when it come to the question of “Where is Paris?” you will have to translate these names into some sort of description of where it is in relation to yourself or a known point in the world.
You can say that Paris is 100km to the east and 50km to the south of you or simply say that it is three days travel on foot in the direction you are pointing or simply give the coordinates and those descriptions are all vectors.
When we ask where is place “x”? We expect an answer that either takes the form of a direction and a distance or some description that can be translated into one.
A step to the right is a vector because it describes a direction “right” and a magnitude “one step”.
A description like “take the third right and then go straight for three blocks” is actually two vectors, which we naturally can sum up to one.
In the real world we often use two dimensional vectors to describe points, because it is understood unless otherwise mentioned that you won’t tunnel into the earth or fly into the air but stay on ground-level. We treat the world as flat, because for the purpose of navigation it mostly is.
Latest Answers