Question

A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector ? The rotation of a body can be specified by the direction of the axis of rotation, and the angle of rotation about the axis. Does that make any rotation a vector?

Answer 1

Generally, rotation is not considered a vector, though it has magnitude and direction. The reason is that addition of two finite rotations does not obey commutative law. Since, addition of vectors should obey commutative law, a finite rotation cannot be regarded as a vector. However, infinitesimally small rotations obey commutative law for addition and hence an infinitesimally small rotation is a vector.