question_answer

Let \[\left| {\vec{a}} \right|=1,\,\left| {\vec{b}} \right|=2,\,\,\left| {\vec{c}} \right|=3\] and \[\vec{a}\bot \left( \vec{b}+\vec{c} \right),\]  \[\,\vec{b}\bot \left( \vec{c}+\vec{a} \right)\] and \[\vec{c}\bot (\vec{a}+\overrightarrow{b})\]. If the value of \[\left| \vec{a}+\vec{b}+\vec{c} \right|\] is \[\sqrt{k}\] then find k.

Answer:

14.00