question_answer

Let PQRS be a parallelogram whose diagonals PR and QS intersect at O?. If O is origin, then \[\overrightarrow{OP}+\overrightarrow{OQ}+\overrightarrow{OR}+\overrightarrow{OS}\]is equal to

A)  \[\overrightarrow{OO'}\]         

B)  \[2\overrightarrow{O}O'\]

C)  \[3\overrightarrow{O}Q'\]       

D)  \[4\overrightarrow{O}O'\]

Correct Answer: D

Solution :

Given, diagonals PR and QS intersect each other at O?, Thus, O? is the mid point of PR and QS and O is origin, \[\therefore \] \[\overrightarrow{OP}+\overrightarrow{OR}=2\overrightarrow{OO}'\] ?..(i) and \[\overrightarrow{OQ}+\overrightarrow{OS}=2\overrightarrow{OO}'\] ??(ii) On adding Eqs. (i) and (ii), we get