Let $\overline{\mathrm{a}}=2\overline{\mathrm{i}}-2\overline{\mathrm{j}}+\overline{\mathrm{k}},\overline{\mathrm{b}}=\overline{\mathrm{j}}+\overline{\mathrm{k}}$. If $\overrightarrow{c}$ is a vector such that $\overline{\mathrm{a}}\cdot \overline{\mathrm{c}}=\overline{|\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}\mid =2\sqrt{2}$ and the angle between $\overline{\mathrm{a}}\times \overline{\mathrm{b}}\text{ and }\overline{\mathrm{c}}$ is 60°, then $\left|\right(\overline{\mathrm{a}}\times \overline{\mathrm{b}})\times \overline{\mathrm{c}}|=$

$\begin{array}{l}\overline{\mathrm{a}}\times \overline{\mathrm{b}}=-3\overline{\mathrm{i}}-2\overline{\mathrm{j}}+2\overline{\mathrm{k}} ,\Rightarrow |\overline{\mathrm{a}}\times \overline{\mathrm{b}}|=\sqrt{17}\\ ,\left|\overline{\mathrm{a}}\right|=3\\ |\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2\sqrt{2}\Rightarrow |\overline{\mathrm{c}}{|}^2+|\overline{\mathrm{a}}{|}^2-2(\overline{\mathrm{c}}\cdot \overline{\mathrm{a}})=8\\ |\overline{\mathrm{c}}{|}^2+9-2|\overline{\mathrm{c}}|-8=0\\ \Rightarrow \left(\right|\overline{\mathrm{c}}|-1{)}^2=0\Rightarrow |\overline{\mathrm{c}}|=1\\ \left|\right(\overline{\mathrm{a}}\times \overline{\mathrm{b}})\times \overline{\mathrm{c}}|=|\overline{\mathrm{a}}\times \overline{\mathrm{b}}|\left|\overline{\mathrm{c}}\right|\sin {60}^{\circ }=\sqrt{17}\left(1\right)\frac{\sqrt{3}}{2}=\frac{\sqrt{51}}{2}\\ \end{array}$