1.2: Vector proof in a quadrilateral

Figure 3 shows quadrilateral $\displaystyle ABCD$ such that

(a) Prove that $\displaystyle \overrightarrow{AB}$ is parallel to $\displaystyle \overrightarrow{DC}$.

The diagonals, $\displaystyle AC$ and $\displaystyle BD$, of the quadrilateral intersect at the point $\displaystyle Y$.

(b) Using a vector method, find $\displaystyle \overrightarrow{AY}$ as a simplified expression in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$.