The problem: Vectors $a$, $b$, $c$ make $60^\circ$ angles with each other. $|a| = 4$, $|b| = 2$, $|c| = 6$. Find the length of $p = a + b + c$.
The only way I can think of $a$, $b$ and $c$ having $60^\circ$ angles with each other is that they form a vertex of a tetrahedron. Then, I can find $|a+b|$ or $|b+c|$ or $|a+c|$ using the law of cosines. But then I can't find $|p|$, because I don't know the angle between the vector I have found and the remaining one.
I would like to get some hints or clues how to solve this, thanks in advance.