For \(\mathbf{r}=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}\) and \(r=|\mathbf{r}|\), simplify the following.

a. \(abla \times(\mathbf{k} \times \mathbf{r})\).

b. \(abla \cdot\left(\frac{\mathrm{r}}{\mathrm{r}}\right)\).

c. \(abla \times\left(\frac{\mathbf{r}}{r}\right)\).

d. \(abla \cdot\left(\frac{\mathbf{r}}{r^{3}}\right)\).

e. \(abla \times\left(\frac{\mathrm{r}}{r^{3}}\right)\).