Let $\mathrm{a}=-\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=-\hat{\mathrm{i}}+\mathrm{j}$ and $\dot{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ be three given vectors. If $\dot{\mathrm{r}}$ is a vector such that $\dot{\mathrm{r}} \times \overrightarrow{\mathrm{b}}=\dot{\mathrm{c}} \times \overrightarrow{\mathrm{b}}$ and $\dot{r} \cdot \dot{a}=0$, then the value of $\dot{r} \cdot \vec{b}$ is