Abstract: Using the global transformation properties of vector operators under rotation operations, this paper presents a classical derivation of the Rodrigues formula satisfied by general vector operators. The formula is then applied to two physical examples: 1. We provide some further analysis regarding one of the main conclusions in \[YAN Er-bin. On the state space of angular momentum. College Physics, 2021, 40(10): 18-21\], 2. Solution of the Rabi problem with the static magnetic field pointing along an arbitrary direction.

Key words: vector operators, spatial rotations, spin component operator, Rabi problem