(a) Prove that the position coordinate \(r\) transforms as a vector under 3D rotations; that is, show that it is an \(\mathrm{SO}(3)\) tensor of rank one. Hint: Begin by noting that the orbital angular momentum may be written in the form \(L_{a}=\epsilon_{a b c} r_{b} p_{c}\), where \(\epsilon_{a b c}\) is the completely antisymmetric rank- 3 tensor, \(r_{b}\) is the position component, and \(p_{c}\) is the momentum component.

(b) Show that the linear momentum transforms as an \(\mathrm{SO}(3)\) vector.