1. Given the position vector, identify the unit vectors in the polar coordinate: \vec{r}(r, \theta)=r \cos \theta \hat{i}+r \sin \theta \hat{j} Using the definitions 1) and 2), solve for 3)

and 4); show you work. \text { 1. } \hat{\boldsymbol{r}}=\frac{\partial \vec{r}}{\partial \boldsymbol{r}} /\left|\frac{\partial \vec{r}}{\partial \boldsymbol{r}}\right| 2 . \hat{\theta}=\frac{\partial \vec{r}}{\partial \theta} /\left|\frac{\partial \vec{r}}{\partial \theta}\right| 3 \hat{i}(\hat{r}, \hat{\theta})=i ? \text { 4. } \hat{j}(\hat{r}, \hat{\theta})=i ?