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Section Formula

In a quadrila...

Question

In a quadrilateral $P Q R S, \to P Q = \to a, \to Q R = \to b, \to S P = \to a - \to b . M$ is the mid-point of $Q R$ and $X$ is a point on $S M$ such that $\to S X = \frac{4}{5} \to S M$ , then $\to P X$ is

A

\frac{1}{5} \to P R

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B

\frac{3}{5} \to P R

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C

\frac{2}{5} \to P R

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D

None of these

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Solution

The correct option is A $\frac{3}{5} \to P R$
Choose $P$ as the origin of reference.
$\to P R = \to a + \to b$ ,
$\to P S = - (\to a - \to b) = \to b - \to a$
$\to P M = \to a + \frac{\to b}{2}$
Given :
$\to S X = \frac{4}{5} \to S M$
$\to P X - (\to b - \to a) = \frac{4}{5} {\to a + \frac{\to b}{2} - (\to b - \to a)}$
$\Rightarrow \to P X = \frac{3}{5} (\to a + \to b)$
$= \frac{3}{5} \to P R$

Hence, option $B .$

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