1.1. Figure 3 shows a sketch of triangle $ABC$.

The point $D$ is the midpoint of $AB$. The point $E$ is the midpoint of $AC$. The line segments $BE$ and $CD$ intersect at the point $F$.

Given that $\overset{\rightarrow}{AB}=2a$ and $\overset{\rightarrow}{AC}=2b$, find $\overset{\rightarrow}{BC}$, $\overset{\rightarrow}{BE}$ and $\overset{\rightarrow}{CD}$ in terms of $a$ and $b$.

1.2. By setting up and solving suitable vector equations, prove that each of the line segments $BE$ and $CD$ divides the other in the ratio $1:2$.