Question: Give an example for which $\vec{A} \cdot \vec{B}=\vec{C} \cdot \vec{B}$ but $\vec{A} \neq \vec{C}$.
Solution:
Let us assume that $B$ is along $Y$ axis, and $A$ is along positive $x$ axis and $C$ is along negative $X$ axis. Now, $A \cdot B=B \cdot C=0$. But $A \neq C$
