In relation to the points $P_{1}$ and $P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin? $$ \mathbf{u}=\overrightarrow{O P_{1}}+\frac{1}{2}\left(\overrightarrow{O P_{2}}-\overrightarrow{O P_{1}}\right) $$