A regular hexagon has a side a. Six particles situated at the corners of the hexagon are

moving with a constant speed v. As per the question, each particle maintains a direction towards the particle at the next corner. So, particles will meet at centroid O of triangle . Now, at any instant, the particles will form an equilateral triangle with the same centroid O. We know that P approaches approaches R and so on.
Now, we will consider the motion of particle P. Its velocity makes an angle of .
This component is the rate of decrease of distance PO.
Relative velocity between P and Q:

Time,

Hence, the time taken by the particles to meet each other is .