In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by three quantities, a unit vector e indicating the direction of an axis of rotation, and an angle θ describing the magnitude of the rotation about the axis. Only two numbers, not three, are needed to define the direction of the unit vector e because its magnitude is constrained. The angle θ scalar multiplied by the unit vector e is the axis-angle vector