Orientation of a vector is 2 dimensions (spherical coordinates), orientation of a 3D object is 3 dimensions (Euler angles). It all boils down to the fact that y

Orientation of a vector is 2 dimensions (spherical coordinates), orientation of a 3D object is 3 dimensions (Euler angles). It all boils down to the fact that you can rotate the vector using itself as its axis and it stays the same, but you can't do that with, say, a cube.