question_answer

The angle between-two vectors \[\vec{A}\]and \[\vec{B}\]is \[\theta \]and their resultant makes an angle \[\frac{\theta }{2}\] with \[\vec{A}.\]Which of the following is true?

A)  A = 2B                      

B) \[A=\frac{B}{2}\]     

C)    A = B             

D)    AB = 1

Correct Answer: C

Solution :

Let the resultant of \[\vec{A}\]and \[\vec{B}\]be \[\vec{R}\]as shown in figure Applying. Sine rule in the triangle we get \[\frac{A}{\sin \alpha }=\frac{B}{\sin \frac{\theta }{2}}\]or, \[\frac{A}{\sin \frac{\theta }{2}}=\frac{B}{\sin \frac{\theta }{2}}\] or \[A=B\] Hence, the correction option is (c).