The angular momentum $\mathbf{L}$ of a particle is defined as the cross product of its position vector $\mathbf{r}$ and linear momentum vector $\mathbf{p}$, i.e., $\mathbf{L} = \mathbf{r} \times \mathbf{p}$. By the right-hand rule of the cross product, the vector $\mathbf{L}$ is perpendicular to the plane containing both $\mathbf{r}$ and $\mathbf{p}$. In orbital motion, $\mathbf{r}$ and $\mathbf{p}$ define the orbital plane. Thus, the angular momentum vector is perpendicular to the orbital plane.