The diagram shows the triangle $OAC$. The point $B$ is the midpoint of $OC$. The point $Y$ lies on $AC$ such that $OY$ intersects $AB$ at the point $X$ where $AX:XB=3:1$. It is given that $\overset{\rightarrow}{OA}=a$ and $\overset{\rightarrow}{OB}=b$.

Find $\overset{\rightarrow}{OX}$in terms of $a$ and $b$, giving your answer in its simplest form.

1.2. Find AC in terms of a and b.

1.3. Given that $\overset{\rightarrow}{OY}=h\overset{\rightarrow}{OX}$ , find $\overset{\rightarrow}{AY}$ in terms of $a$, $b$ and $h$.

1.4. Given that $\overset{\rightarrow}{AY}=m\overset{\rightarrow}{AC}$, find the value of $h$ and of $m$.