is anybody out there who can help with this little problem? I know the definition of inner product space, but I don't know how to do the proof of the exercise below.

Let $a,b,c$ be elements of an inner product space. Show that the following equality
$$
\|a-c\|=\|a-b\|+\|c-b\|
$$ holds iff there exists a real number $\mu\in[0,1]$ s.t. $b=\mu a+(1-\mu)c$.

Can you give an example that shows that this is not true in an arbitrary normed space?