question_answer

Let \[\vec{a}=2\,\hat{i}+\hat{j}-2\hat{k}\] and \[\vec{b}=\hat{i}+\hat{j}.\] If \[\overrightarrow{c}\] is a vector such that \[\vec{a}.\vec{c}=\left| {\vec{c}} \right|,\left| \vec{c}-\vec{a} \right|=2\sqrt{2}\] and the angle between \[\vec{a}\times \vec{b}\] and \[\overrightarrow{c}\] is \[30{}^\circ ,\] then find value of \[\left| \left( \vec{a}\times \vec{b} \right)\times \vec{c} \right|.\]

Answer:

1.50