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

Question

( A ) $\overrightarrow{a} . \overrightarrow{b} = \overrightarrow{b} . \overrightarrow{c} = \overrightarrow{c} . \overrightarrow{a} = 0$
( B ) $\overrightarrow{a} . \overrightarrow{b} = \overrightarrow{b} . \overrightarrow{c} = \overrightarrow{c} . \overrightarrow{b} = 0$
( C ) $\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{c} \times \overrightarrow{a}$
( D ) $\overrightarrow{a} \times \overrightarrow{a} + \overrightarrow{a} \times \overrightarrow{c} + \overrightarrow{c} \times \overrightarrow{a}=0$