$P Q R S$ is a parallelogram. If $\overrightarrow{P R}=\vec{a}$ and $\overrightarrow{Q S}=\vec{b}$, then what is $\overrightarrow{P Q}$ equal to?

• A

  $\vec{a}+\vec{b}$
• B

  $\vec{a}-\vec{b}$
• C

  $\frac{\vec{a}+\vec{b}}{2}$
• Correct answer
  D

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

Solution

$\begin{aligned} & \overrightarrow{P Q}=\overrightarrow{P O}-\overrightarrow{Q O} \\ & =\frac{\vec{a}}{2}-\frac{\vec{b}}{2}=\frac{1}{2}(\vec{a}-\vec{b})\end{aligned}$

Hence, the correct answer is option: 'D'.