question_answer

P is a point on the side BC of the \[\Delta \,ABC\] and Q is a point such that \[\overrightarrow{PQ}\] is the resultant of \[\overrightarrow{AP},\,\overrightarrow{PB},\,\overrightarrow{PC}.\] Then ABQC is a

A) Square   

B) Rectangle

C) Parallelogram

D) Trapezium

Correct Answer: C

Solution :

\[\overrightarrow{AP}+\overrightarrow{PB}+\overrightarrow{PC}=\overrightarrow{PQ}\] or \[\overrightarrow{AP}+\overrightarrow{PB}=\overrightarrow{PQ}+\overrightarrow{CP}\] or  \[\overrightarrow{AB}=\overrightarrow{CQ}\]. Hence it is a parallelogram.