question_answer

If \[\vec{A},\vec{B}\] and \[\vec{C}\] are non-zero vectors and \[\vec{A}.\vec{B}=0\] and \[\vec{B}.\vec{C}=0,\] then find out the value of \[\vec{A}.\vec{C}\]. 

Answer:

                \[\vec{A}.\vec{B}=0\]  \[\Rightarrow \] \[\vec{A}\bot \vec{B}\]                 \[\vec{B}.\vec{C}=0\]  \[\Rightarrow \]  \[\vec{B}\bot \vec{C}\] \[\therefore \]  \[\vec{A}||\vec{C}\] and\[\vec{A}.\vec{C}=AC\,\cos 0{}^\circ =AC.\]