Question

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

• A. Square
• B. Rectangle
• C. Parallelogram
• D. Trapezium

Answer 1

Answer: (C)

Parallelogram

Answer 2

$\overset{\rightarrow}{AP} + \overset{\rightarrow}{PB} + \overset{\rightarrow}{PC} = \overset{\rightarrow}{PQ}$ or $\overset{\rightarrow}{AP} + \overset{\rightarrow}{PB} = \overset{\rightarrow}{PQ} + \overset{\rightarrow}{CP}$

or $\overset{\rightarrow}{AB} = \overset{\rightarrow}{CQ}$.

Hence it is a parallelogram.