Need a hint: the sum of vectors is zero and their norms are equal? Vectors $a$, $b$ and $c$ all have length one. $a + b + c = 0$. Show that 
$$
|a-c| = |a-b| = |b-c|
$$
I am not sure how to get started, as writing out the norms didn't help and there is no way to manipulate 
$$
|a-c| \le |a-b| + |b-c|
$$ 
to get an equality. I just need an idea of where to start.

Hint: 
\begin{equation*}
\langle a,a + b + c \rangle = 0.
\end{equation*}
