Let i =2 i + j -2 k and b = i + j . if c is a vector such that a c =| c |,| c - a |=2 2…

Let \(\overrightarrow{\mathbf{i}}=2 \hat{i}+\hat{j}-2 \hat{k} \text { and } \vec{b}=\hat{i}+\hat{j} \text {. if } \vec{c}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{c}}=|\overrightarrow{\mathrm{c}}|,|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathbf{a}}|=2 \sqrt{2}\) and the angle between \((\vec{a} \times \vec{b}) \text { and } \vec{c} \text { is } 30^{a} \text {, then }|(\vec{a} \times \vec{b}) \times \vec{c}|\) is equal to :