Prove that $\overrightarrow{AQ}=\overrightarrow{BQ}$ $\implies$ $A=B$

Question

Prove that $\overrightarrow{AQ}=\overrightarrow{BQ}$ $\implies$ $A=B$.

My doubt is whether it is a question that must be solved by algebraism or just by definitions...

Answer 1

$$\overrightarrow{AQ}=\overrightarrow{BQ}\implies \overrightarrow{AB}=\overrightarrow{BQ}-\overrightarrow{AQ}=0$$ and $$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=0$$ $$\implies\overrightarrow{OA}=\overrightarrow{OB}\implies A=B$$