Let a =2 i + j -2 k, b = i + j. If c is a vector such that a · c =| c |,| c - a |=2 √ 2 and the angle between a × b and c is 30°, then |( a × b ) × c…

Let $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}+\hat{j}-2 \hat{k}, \overrightarrow{\mathrm{~b}}=\hat{i}+\hat{j}$. If $\displaystyle \overrightarrow{\mathrm{c}}$ is a vector such that $\displaystyle \vec{a} \cdot \vec{c}=|\vec{c}|,|\vec{c}-\vec{a}|=2 \sqrt{2}$ and the angle between $\displaystyle \vec{a} \times \vec{b}$ and $\displaystyle \vec{c}$ is $\displaystyle 30$°, then $\displaystyle |(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}|$ equals :