Vedas are called ‘Trayi’ which do not refer to its divisions. It has become quite clear from the ancient philosophies that Vedas in its initial period was only one. It was only in the later days that it was classified into 4 parts.
According to historians and great scholars when the mankind gave importance more to sacrifices than meditation, then for the convenience of accomplishment of sacrifice Veda was divided into 4 parts.
As per the religious beliefs, sacrifices from Rig Veda, Adhvaryu from Yajurveda and Brahma from Atharv Veda complete their share of work.
There are mainly two reasons behind the Vedas being called Trayi firstly, the mantras in the 4 Vedas are of three types: (i) of Viniyoga (ii) of songs (iii) of prose; secondly, the entire Vedas relate three kinds of things: (i) Gyankand (knowledge) (ii) Upasana kand (worship) (iii) Karma kand (action). Hence Vedas are called Trayi.