Question

Three vectors $\vec{P}$, $\vec{Q}$ and $\vec{R}$ are shown in the figure. Let $𝑆$ be any point on the vector $\vec{R}$. The distance between the points $𝑃$ and $𝑆$ is $b|\vec{R}|$. The general relation among vectors $\vec{P}$, $\vec{Q}$ and $\vec{S}$ is

• A. $\vec{S} = \left(1-b\right)\vec{P} + b\vec{Q}$
• B. $\vec{S} = \left(b-1\right)\vec{P} + b\vec{Q}$
• C. $\vec{S} = \left(1-b^{2}\right)\vec{P} + b\vec{Q}$
• D. $\vec{S} = \left(1-b\right)\vec{P} + b^{2}\vec{Q}$

Answer 1

Answer: (A)

$\vec{ S }-\vec{ P }= b \vec{ R }$
and $\vec{ Q }-\vec{ S }=(1- b ) \vec{ R }$
where $\vec{ R }=\vec{ Q }-\vec{ P }$
From these two equations
$\vec{ S }=(1- b ) \vec{ P }+ b \vec{ Q }$