Three vectors $\vec{P}, \vec{Q}$ and $\vec{R}$ are shown in the figure. Let $S$ be any point on the

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

Professor PC Thomas Classes · Answer

(a): Given: $P S=b|\vec{R}|, \vec{R}=\vec{Q}-\vec{P}$ Using law of vector addition, \ $ \begin{aligned} & \vec{P}+\overrightarrow{P S}=\vec{S} \ & \Rightarrow \quad|\vec{P}| \hat{P}+b|\vec{R}| \hat{R}=S \hat{S} \ & 	herefore \quad \vec{P}+b \vec{R}=\vec{S} \ & 	ext { or } \quad \vec{P}+b(\vec{Q}-\vec{P})=\vec{S} \ & \Rightarrow \quad \vec{P}(1-b)+b \vec{Q}=\vec{S} \end{aligned} $