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
$\vec{S}=(1-b)\vec{P}+b\vec{Q}$