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.

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.