Vector Algebra

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be three vectors. If $\mathbf{r}$ is a vector such that $\mathbf{r} \cdot \mathbf{a}=0$, $\mathbf{r} \cdot \mathbf{b}=-2$ and $\mathbf{r} \cdot \mathbf{c}=6$, then $\mathbf{r} \cdot(\beta \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=$