how we can classify b/w infinite and finite angular displacement

Finite angular displacements are not vector quantities, the reason being that they do not obey the law of vector addition. This law asserts that the order in which vectors are added does not affect their sum.
However finite angles under addition tend towards commutivity as the angles become very small. Infinitesimal angles do commute under addition, making it possible to treat them as vectors.

whereas infinitesimal angular displacement satisfies both so is a true vector.
By infinitesimal angular displacement, the tip of the position-vector moves in a straight line. So, this angular displacement has a definite direction. Hence, it is a vector.

Approved