Question

Two vectors, each of magnitude $A$ have a resultant of same magnitude $A$. The angle between the two vectors is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is C ${120}^{\circ }$

According to the question,

$R=A=\sqrt{A^2+A^2+2A.Acos\theta }$

$A^2=A^2+A^2+2A.Acos\theta$

$A^2=2A^2+2A^{2}cos\theta$

$1=2(1+cos\theta )$

$1+cos\theta =\frac{1}{2}$

$cos\theta =-\frac{1}{2}=-0.5$

$\theta =co{s}^{-1}(-0.5)$

$\theta ={120}^0$

The correct option is C.