question_answer

If the vectors \[\overrightarrow{a},\] \[\overrightarrow{b}\] and \[\overrightarrow{c}\] from the sides BC, CA and AB respectively of a triangle ABC, then

A)  \[\overrightarrow{a}.\overrightarrow{b}=\overrightarrow{b}.\overrightarrow{c}=\overrightarrow{c}.\overrightarrow{b}=0\]

B)  \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{c}\times \overrightarrow{b}\]

C)  \[\overrightarrow{a}.\overrightarrow{b}=\overrightarrow{b}.\overrightarrow{c}=\overrightarrow{c}.\overrightarrow{a}=0\]

D)  \[\overrightarrow{a}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a}=\overrightarrow{0}\]

E)  None of these