Search any question & find its solution
Question:
Answered & Verified by Expert
$P Q R S$ is a quadrilateral and $\mathbf{P Q}=\mathbf{a}, \mathbf{Q R}=\mathbf{b}, \mathbf{S P}=\mathbf{a}-\mathbf{b}, M$ is the mid-point of $Q R$ and $X$ is a point on $\mathbf{S M}$ such that $\mathbf{S X}=\frac{4}{5} \mathbf{S M}$. If $\mathbf{S M}=m(4 \mathbf{a}-\mathbf{b})$ and $\mathbf{S X}=n(4 \mathbf{a}-\mathbf{b})$, then $m+n=$
Options:
Solution:
2830 Upvotes
Verified Answer
The correct answer is:
$9 / 10$
$\begin{aligned} & S Q=S P+P Q=(a-b)+a=2 a-b \\ & S M=S Q+Q M=(2 a-b)+\frac{b}{2}=2 a-\frac{b}{2}\end{aligned}$
$\Rightarrow \quad \mathbf{S M}=\frac{1}{2}(4 \mathbf{a}-\mathbf{b})$
$\therefore \quad m=\frac{1}{2}$
$\mathbf{S X}=\frac{4}{5} \mathbf{S M}$ (given)
$=\frac{4}{5} \cdot \frac{1}{2}(4 a-b)$
$\Rightarrow \quad S X=\frac{2}{5}(4 a-b)$
$\therefore \quad n=\frac{2}{5}$
Hence, $m+n=\frac{1}{2}+\frac{2}{5}=\frac{9}{10}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.