Vector Algebra

Let \(\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}\) and \(\bar{c}\) be a vector such that \(|\bar{c}-\bar{a}|=4,|(\bar{a} \times \bar{b}) \times \bar{c}|=3\) and the angle between \(\overline{\mathrm{c}}\) and \(\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) is \(\frac{\pi}{6}\), then \(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}\) is equal to