Instead of representing a change of orientation by three separate rotations, quaternions use just one rotation. This saves time and storage and also solves the problem of gimbal lock.

While a phone or arrow turns all the way around in 360 degrees, the quaternion describing this 360-degree rotation only turns 180 degrees up in four-dimensional space.

The vector is an important idea, and the quaternion is an important idea, but there are in physical science many other important ideas which call for a more direct notation.

Weina Wu, Zhong You, Modelling rigid origami with quaternions and dual quaternions, Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 466, No. 2119 (8 July 2010), pp. 2155-2174 ...