Solution
= Solution
The third particle is force-free, so its <torque> about the origin vanishes:
$$
\frac d{dt}\left(m_3\mathbf q_3\times\dot{\mathbf q}_3\right)
=\mathbf q_3\times m_3\ddot{\mathbf q}_3=0.
$$
Thus \b[this <angular momentum> is conserved].