\begin{eqnarray*}
\vec{v} & = & \vec{a} + \vec{b} \\
 & = & (a.x + b.x, a.y + b.y) \\
 \vec{v} & = & p2 - p1 \\
 & = & (p2.x - p1.x, p2.y - p1.y) \\
 -\vec{a} & = & (-a.x, -a.y) \\
\vec{v} & = & s \cdot \vec{a} \\
 & = & (s \cdot a.x, s \cdot a.y) \\
|\vec{a}| & = & \sqrt{a.x^2+a.y^2} \\
 \hat{a} & = & \left(\frac{a.x}{|\vec{a}|}, \frac{a.y}{|\vec{a}|} \right)
\end{eqnarray*}