Let a =6 i + j - k and b = i + j. If c is a is vector such that | c | ≥ 6, a · c =6| c |,| c - a |=2 √ 2 and the angle between a × b and c is 60^°,…

Let $\displaystyle \overrightarrow{\mathrm{a}}=6 \hat{i}+\hat{j}-\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{b}}=\hat{i}+\hat{j}$. If $\displaystyle \overrightarrow{\mathrm{c}}$ is a is vector such that $\displaystyle |\overrightarrow{\mathrm{c}}| \geq 6, \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=6|\overrightarrow{\mathrm{c}}|,|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|=2 \sqrt{2}$ and the angle between $\displaystyle \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ and $\displaystyle \overrightarrow{\mathrm{c}}$ is $\displaystyle 60^{\circ}$, then $\displaystyle |(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}|$ is equal to: