OABC is a parallelogram. If $\vec{OB} = \vec a$ and $\vec{AC} =\vec b$, then $\vec{OA}$ is equal to
Answer & explanation
Correct answer: option 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
$\vec{OA}+\vec{AX}=\vec{OX}$
$\vec{OA}=\vec{OX}-\vec{AX}$
$=\frac{\vec a-\vec b}{2}$