Vector Algebra

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