question_answer

If vectors P, Q and R have magnitude 5, 12 and 13 units and \[\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R},\] the angle between Q and R is [CEET 1998]

A)                 \[{{\cos }^{-1}}\frac{5}{12}\]

B)                                 \[{{\cos }^{-1}}\frac{5}{13}\]

C)                 \[{{\cos }^{-1}}\frac{12}{13}\]    

D)                 \[{{\cos }^{-1}}\frac{7}{13}\]

Correct Answer: C

Solution :

                    \[|\vec{P}|\ =\ 5\], \[|\vec{Q}|\ =12\] and \[|\vec{R}|\ =13\]                 \[\cos \theta =\frac{Q}{R}=\frac{12}{13}\]                  \ \[\theta ={{\cos }^{-1}}\left( \frac{12}{13} \right)\]