Let $\vec{a}=\hat{i}+2 \hat{j}-\hat{k}, \vec{b}=\hat{i}-\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a}=\vec{c} \times \vec{a}$ an $\overline{\mathrm{r}} \cdot \overline{\mathrm{b}}=0$ then $\overline{\mathrm{r}} \cdot \overline{\mathrm{a}}$ is equal to $\_\_\_\_$ .