question_answer

Let vectors \[\vec{a}=-\hat{i}+\hat{j}+\hat{k},\] \[\vec{b}=2\hat{i}+\hat{k}\] and \[\vec{c}\] be such that \[[\vec{a}\,\vec{b}\,\vec{c}]=0,\] \[\vec{b}\,.\,\vec{c}=0\] and \[\vec{a}\,.\,\vec{c}=7\]. Then the value of \[\frac{2}{7}|\vec{c}{{|}^{2}}\] is

Answer:

5