Let $\vec{a} = -2\hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$, and $\vec{c} = 2\hat{i} - 3\hat{j} + 4\hat{k}$. A vector $\vec{r}$ satisfying $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$ is: