Q. The position vectors of $P$ and $Q$ are respectively $\overrightarrow{\mathbf{a}}\$and $\overrightarrow{\mathbf{b}}$ .If R is a point on $\overrightarrow{\mathbf{PQ}}\$such that $\overrightarrow{\mathbf{PR}} = 5\overrightarrow{\mathbf{PQ}}\ ,\$then the position vector of $R$ is
A) $5\overrightarrow{\mathbf{b}} - 4\overrightarrow{\mathbf{a}}\$
B) $5\overrightarrow{\mathbf{b}} + 4\overrightarrow{\mathbf{a}}\$
C) $4\overrightarrow{\mathbf{b}} - 5\overrightarrow{\mathbf{a}}\$
D) $4\overrightarrow{\mathbf{b}} + 5\ \overrightarrow{\mathbf{a}}\$
Explanation
(a)
Given $\overrightarrow{\mathbf{PR}} = 5\overrightarrow{\mathbf{PQ}}$
It means $R$ divides $PQ$ extrenally in the ratio 5:4
$\therefore\ \ Position\ vector\ of\ R\frac{5\overrightarrow{\mathbf{b}} - 4\overrightarrow{\mathbf{a}}}{5 - 4}$
$= 5\overrightarrow{\mathbf{b}} - 4\overrightarrow{\mathbf{a}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.