I'm reading a book on analytic geometry, specifically on a chapter on change of coordinates. It says that having the origin $O$, one point $P$ and a new origin $O'$, the vector that describes the point $P$ in relation to the new origin $O'$ is:
$$O'P=OP-OO'$$
I'm in doubt: Will it always be $OP-OO'$? I mean, why it couldn't be $OP+OO'$ or $OO'-OP$ or $OO'+OP$? I've made some experiments to understand why is that (I know that it's due to some basic property of expression of sums of vectors) but the only explanation I could find is that we're pulling $P$ from $O'$, then the sum need to be that way. But my own explanation doesn't seem too precise nor meaningful.