Ezekiel 1:12

went straightforward i.e. in the direction to which the living creature's face was turned. The chariot had four sides facing the four quarters of the heavens; on each side of the chariot was a living creature whose principal face, the human, looked in the same direction as the side of the chariot on which it stood. Thus the whole, the chariot and living creatures, presented exactly the same front to each of the four directions, and there was no need to "turn." See what is said of the wheels, Ezekiel 1:15 seq.

whither the spirit was to go The "spirit" is the directing impulse. It did not belong to the individual living creatures but to the whole manifestation composed of living creatures, wheels, and the like.