Dipole moment of water using the definition In many Chemistry books, the dipole moment of molecules is calculated through algebraic formulas. However, another definition of the dipole moment is 

$$\vec{\mu} = \sum_i q_i \, \vec{r}_i$$

So, how can we calculate the dipole moment of water, for example using this formula? Is there a difference in interpretation of dipole moment in Physics and Chemistry?

Here is the Definition.
Is there a difference in interpretation of dipole moment in Physics and Chemistry?

Addressing the above part: The definition of dipole moment is the same in physics and chemistry. However, the chemist's dipole moment has opposite directions as compared to the physicist. Which one is right? Of course, the physicists draw it correctly, which is consistent with electrostatics. There was a nice single paged article in the Journal of Chemical Education on this topic. A must read.
Misconceptions in Sign Conventions: Flipping the Electric Dipole Moment
James W. Hovick J. C. Poler
https://pubs.acs.org/doi/10.1021/ed082p889