[QUE/CM-02025]

Prove that quantity defined by \begin{equation} (\vec{M}.\vec{B}) + \frac{e}{2c}[(\vec{r}\times \vec{B}) \cdot (\vec{r}\times \vec{B})]), \qquad \text{where} \vec{M} = m \vec{r}\times\vec{v}. \end{equation} is a constant of motion for a charged particle moving in a uniform magnetic field \(\vec{B}\),