Question

Let $O$ be the origin and $P,Q,R$ be the points such that $\overrightarrow{PQ}+\overrightarrow{OQ}=\overrightarrow{QO}+\overrightarrow{OR}$ .
Then which one of the following is correct ?

• A. P, Q, R are the vertices of an equilateral triangle
• B. P, Q, Rare the vertices of an isosceles triangle
• C. P, Q, R are collinear
• D. None of the above

Answer 1

The correct option is D None of the above

Given condition

$\overrightarrow{PQ}+\overrightarrow{OQ}=\overrightarrow{QO}+\overrightarrow{OR}$

$\overrightarrow{PQ}+\overrightarrow{OQ}-\overrightarrow{OR}=\overrightarrow{QO}$

$\overrightarrow{PQ}+\overrightarrow{RQ}=-\overrightarrow{OQ}$

$\overrightarrow{PQ}+\overrightarrow{RQ}+\overrightarrow{OQ}=0$

It is not condition for triangle $\overrightarrow{PQ}+\overrightarrow{QR}+\overrightarrow{RQ}=0$

It is not collinear point