Vector Algebra

Let \(\overrightarrow a = 2\widehat i + \widehat j - 2\widehat k\) and \(\overrightarrow b = \widehat i + \widehat j\). If \(\overrightarrow c\) is a vector such that \(\overrightarrow a .\,\overrightarrow c = \left| {\overrightarrow c } \right|,\left| {\overrightarrow c - \overrightarrow a } \right| = 2\sqrt 2\) and the angle between \((\overrightarrow a \times \overrightarrow b )\) and \(\overrightarrow c\) is \({\pi \over 6}\), then the value of \(\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right|\) is :