Will they ever meet?

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.