Question

If vectors P, Q and R have magnitude 5, 12 and 13 units and $\overset{\rightarrow}{P} + \overset{\rightarrow}{Q} = \overset{\rightarrow}{R},$ the angle between Q and R is

• A. $\cos^{- 1}\frac{5}{12}$
• B. $\cos^{- 1}\frac{5}{13}$
• C. $\cos^{- 1}\frac{12}{13}$
• D. $\cos^{- 1}\frac{7}{13}$

Answer 1

Answer: (C)

$\cos^{- 1}\frac{12}{13}$

Answer 2

$|\overrightarrow{P}|\mspace{6mu} = \mspace{6mu} 5$, $|\overrightarrow{Q}|\mspace{6mu} = 12$ and $|\overrightarrow{R}|\mspace{6mu} = 13$

$\cos\theta = \frac{Q}{R} = \frac{12}{13}$

∴ $\theta = \cos^{- 1}\left( \frac{12}{13} \right)$