1. $OAB$ is a triangle.

$\overset{\rightarrow}{OA}=a$

$\overset{\rightarrow}{OB}=b$

The point $C$ lies on $OA$ such that $OC:CA=1:2$
The point $D$ lies on $OB$ such that $OD:DB=1:2$

Using a vector method, prove that $ABDC$ is a trapezium.