Q73 / 150 · MHT CET 2017 · Mathematics

Let $P Q R S$ be a quadrilateral. If $M$ and $N$ are midpoints of the sides $P Q$ and $R S$ respectively then $\vec{P S} + \vec{Q R} =$

A
$3 \vec{M N}$
B
$4 \vec{M N}$
Correct answer
C
$2 \vec{M N}$
D
$5 \vec{M N}$

Solution

\bar{m} = \frac{\bar{p} + \bar{q}}{2}

\bar{n} = \frac{\bar{r} + \bar{s}}{2}

\bar{P S} + \bar{Q R} = (\bar{S} - \bar{p}) + (\bar{r} - \bar{q})

= (\bar{r} + \bar{s}) - (\bar{p} + \bar{q})

= 2 \bar{n} - 2 \bar{m}

= 2 (\bar{n} - \bar{m})

= 2 \bar{M N}

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

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