Figure 3 shows triangle $OAB$ with $\overset{\rightarrow}{OA}=a$ and $\overset{\rightarrow}{OB}=b$

$M$ is the midpoint of $OA$.

$N$ is the point on $OB$ such that $ON:NB=3:1$

The lines $AN$ and $BM$ intersect at the point $X$.

Find expressions, in terms of $a$and $b$, for

(i) $\overset{\rightarrow}{AN}$

(ii) $\overset{\rightarrow}{BM}$

1.2. Using a vector method, find $AX:XN$