Three vectors → P , → Q and → R are shown in the figure. Let, S be...

Let, vector from point $P$ to point $S$ be $\overset{\to}{C}$, 

⇒ \overset{\to}{C} = b\left|\overset{\to}{R}\right|\overset{^}{R} = b\left|\overset{\to}{R}\right|\left(\overset{\to}{R}\left|\overset{\to}{R}\right|\right) = b\overset{\to}{R} = b\left(\overset{\to}{Q} - \overset{\to}{P}\right)

From triangle rule of vector addition, 

$\overset{\to}{P} + \overset{\to}{C} = \overset{\to}{S}$

$\overset{\to}{P} + b\left(\overset{\to}{Q} - \overset{\to}{P}\right) = \overset{\to}{S}$

$⇒ \overset{\to}{S} = \left(1 - b\right)\overset{\to}{P} + b\overset{\to}{Q}$