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 \(\bar{a} \cdot \bar{c}=|\bar{c}|,|\bar{c}-\bar{a}|=2 \sqrt{2}\) and the angle between \(\bar{a} \times \bar{b}\) and \(\bar{c}\) is \(\frac{2 \pi}{3}\), then \(|(\bar{a} \times \bar{b}) \times \bar{c}|=\)