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

Explanation

No. There are certain phusical quantities which have both magnitude and direction, but they are bot vectors as they do not follw the laws of vectos addition, which is essential for vectors. The finite rotation of a body about an axis is bot a vector because the finite rotations do not obey the laws of vectors addition.
However, the small rotation of a body ( i.e. samall angle of rotation) is a vector quantity as it obeys the law of vecors addition.