. Prove the following vector identities by whichever method you find convenient to use \text { (a) } \nabla f\left(\mathbf{r}-\mathbf{r}^{\prime}\right)=-\nabla^{\prime} f\left(\mathbf{r}-\mathbf{r}^{\prime}\right) \text {. } \text { (b) } \nabla \cdot[\mathbf{A}(r) \times r]=0 \text {. } \text { (c) } \mathbf{d}=(d \mathbf{d} \cdot \nabla) \mathbf{Q} \text { where } \mathbf{Q} \text { is a differential change in } \mathbf{Q} \text { and } d s \text { is an element of arc length. } (d) Use the Levi-Civitá symbol to prove that b = (b·ôn)în+ân×(b×ôn) and interpret the decompositiongeometrically.