Let a = i +2 j - k, b = i - j and c = i - j - k be three given vectors. If r is a vector such that r × a = c × a and r · b =0, then r · a is equal to…

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