question_answer

If \[\left| \overrightarrow{a} \right|\text{=}3,\left| \overrightarrow{b} \right|=1,\left| \overrightarrow{c} \right|=4\] and \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,\] then find the value of \[\overrightarrow{a\,.\,}\overrightarrow{b}+\overrightarrow{b}\,.\,\overrightarrow{c}+\overrightarrow{c\,}.\,\overrightarrow{a}.\]

A)  13                   

B)  42           

C)  0                    

D)  -13