Answer
See explanation
Work Step by Step
Look at the attached figure. We will use these vectors to represent the sides and diagonals of a parallelogram. Observe that $\mathbf{a}-\frac{1}{2}\left(\mathbf{a}+\mathbf{b}\right)=\frac{1}{2}\left(\mathbf{a}-\mathbf{b}\right).$ Geometrically this means that the vector joining the midpoint of the red diagonal $(\mathbf{a}+\mathbf{b})$ to the tip of $\mathbf{a}$ is exactly the vector pointing from the midpoint of the green diagonal $(\mathbf{a}-\mathbf{b})$ to the tip of $\mathbf{a}$.
