Let $\vec{a} = 2\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \hat{j}$. Let $\vec{c}$ be a vector such that $|\vec{c} - \vec{a}| = 3$ and $|(\vec{a} \times \vec{b}) \times \vec{c}| = 3$, and the angle between $\vec{c}$ and $\vec{a} \times \vec{b}$ is $30^\circ$. Then, $\vec{a} \cdot \vec{c}$ is equal to