Question

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

• A. ${60}^{\circ }$
• B. ${90}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

From the triangle law of vector addition, it is clear that the vectors R, A and B must be represented by the three sides of an equilateral triangle because the magnitudes of the three vectors are equal. Hence the angle $\alpha$ between vectors R and A is ${60}^{\circ }$. Alternatively, the value of $\alpha$ is given by
$\tan \alpha =\frac{B\sin \theta }{A+B\cos \theta }=\frac{\sin \theta }{1+\cos \theta }(\because A=B)$
$=\frac{\sin {120}^{\circ }}{1+\cos {120}^{\circ }}=1.732$
Which gives $\alpha ={60}^{\circ }.$
Hence the correct choice is (a)