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1. The problem statement, all variables and given/known data

Say you have two reference frames R_1 and R_2, where the origin of R_2 is far away from the origin of R_1. Then say you have a point in space P. The position vector of P in R_1 is r_1 and the position vector of P in R_2 is r_2.

What I am confused about is that vectors are supposed to be tensors which are supposed to be geometric objects that are invariant under coordinate transformations, right? Only their components change. But when you look at r_1 it is not the same as r_2. I don't understand that?

This is from Wikipedia: "The intuition underlying the tensor concept is inherently geometrical: as an object in and of itself, a tensor is independent of any chosen frame of reference."

What am I missing?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Position vectors

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