• # 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

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).