Taylor expansion of a vector function

1. Apr 4, 2013

xBorisova

Could someone please explain how does this taylor expansion work:
1/|r-r'| ≈ 1/r+(r.r')/r3

possibly you have to taylor expand twice to get this result, an attempt at which led me nowhere,
surely it cannot be this complicated.

thank you

2. Apr 4, 2013

TSny

Hello, xBorisova. Welcome to PF!

As a hint, note that for any vector $\textbf{A}$, $|\textbf{A}| = \sqrt{\textbf{A}\cdot \textbf{A}}$.