Will they ever meet?

Classical Mechanics Level 4

Consider three particles $P,Q,R$ which are situated at the vertices of equilateral triangle $ABC$ of side $1\text{ m}$ .Each of the particles move with constant speed $1 \text{ m/s}$ . $P$ always has its velocity along $AB$ , $Q$ always has its velocity along $BC$ , $R$ always has its velocity along $CA$ . At what time in seconds will the particles meet each other?

If you think that they will never meet , prove it and enter the answer as 1.1.
If you think that they will meet at infinity , prove it and enter the answer as 2.2.