question_answer

 The magnitudes of vectors \[\vec{A},\,\vec{B}\]and\[\vec{C}\]are 3, 4 and 5 units respectively. If \[\vec{A}+\vec{B}=\vec{C}\], the angle between \[\vec{A}\]and \[\vec{B}\]is                                                                 [CBSE PMT 1990]

A)                 \[\frac{\pi }{2}\]

B)                 \[{{\cos }^{-1}}(0.6)\]

C)                 \[{{\tan }^{-1}}\left( \frac{7}{5} \right)\]               

D)                 \[\frac{\pi }{4}\]

Correct Answer: A

Solution :

                    \[C=\sqrt{{{A}^{2}}+{{B}^{2}}}\]                                 =\[\sqrt{{{3}^{2}}+{{4}^{2}}}=5\]                 \[\therefore \] Angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is \[\frac{\pi }{2}\]