Vector Algebra

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