Question 96
Suppose the included angle between non-zero vectors $\vec{a}$ and $\vec{b}$ in the plane is $\frac{\pi}{3}$. If $|\vec{a}|, |\vec{b}|, |\vec{a} + \vec{b}|$ form arithmetic sequence in order, find the value of $|\vec{a}| : |\vec{b}| : |\vec{a} + \vec{b}|$.