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 point $P$ and $S$ is $b|\vec{R}|$. The general relation among vectors $\vec{P}, \vec{Q}$ and $\vec{S}$ is

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