Let \(\vec{a}=2\overset{^}{i}+\overset{^}{j}-2\overset{^}{k}\) and \(\vec{b}=\overset{^}{i}+\overset{^}{j}\). If \(\vec{…

Let \(\vec{a}=2\overset{^}{i}+\overset{^}{j}-2\overset{^}{k}\) and \(\vec{b}=\overset{^}{i}+\overset{^}{j}\). If \(\vec{c}\) is a vector such that \(\vec{a}\cdot \vec{c}=|\vec{c}|,|\vec{c}-\vec{a}|=2\sqrt{2}\) and the angle between \((\vec{a}\times \vec{b})\) and \(\vec{c}\) is \({30}^{0}\), then the value of \(|(\vec{a}\times \vec{b})\times \vec{c}|\) is :

[JEE Main 2021, 20 Jul (Shift 1)]