# 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 $\textbf{A}$, $|\textbf{A}| = \sqrt{\textbf{A}\cdot \textbf{A}}$.