OABC is a parallelogram. If $\vec{OB} = \vec a$ and $\vec{AC} =\vec b$, then $\vec{OA}$ is equal to

$\frac{\vec a-\vec b}{2}$

$\vec{OB} = \vec a$

$\vec{AC} =\vec b$

$\vec{OA}=?$

$\vec{OX}=\frac{\vec{OB}}{2}=\frac{\vec a}{2}$

$\vec{AX}=\frac{\vec{AC}}{2}=\frac{\vec b}{2}$ diagonals of parallelogram bisect each other

so by triangular law of vector addition

$\vec{OA}+\vec{AX}=\vec{OX}$

$\vec{OA}=\vec{OX}-\vec{AX}$

$=\frac{\vec a-\vec b}{2}$