Vector Algebra

The vectors are \(\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \bar{b}=\hat{i}+\hat{j}\). If \(\bar{c}\) is a vector such that \(\bar{a} \cdot \bar{c}=|\bar{c}|\) and \(|\bar{c}-\bar{a}|=2 \sqrt{2}\), angle between \(\bar{a} \times \bar{b}\) and \(\bar{c}\) is \(\frac{\pi}{4}\), then \(|(\bar{a} \times \bar{b}) \times \bar{c}|\) is