Using Eq. (11.140), show that if we use G= L x as a generator of a transformation (where (L_{x}) is the (x)-component of the angular

Using Eq. (11.140), show that if we use G= ϵL_x as a generator of a transformation (where \(L_{x}\) is the \(x\)-component of the angular momentum), we end up rotating the components of the position vector \(\mathbf{r}\) by an infinitesimal angle \(\epsilon\) about the \(x\)-axis. Show this by applying the generator onto an arbitrary function of position \(A(\mathbf{r})\). Similarly, find the generators that rotate the position vector about the \(y\) and \(z\)-axes.