Question

If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vectors, then the angle between two vectors is

• A. ${125}^o$
• B. ${130}^o$
• C. ${110}^o$
• D. ${120}^o$

Answer 1

The correct option is D ${120}^o$

Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be given two vectors.
$|\overrightarrow{A}|=|\overrightarrow{B}|=|\overrightarrow{R}|$ = x(say)
$R=\sqrt{A^2+B^2+2AB\cos \theta }$
$x^2=x^2+x^2+2x^2\cos \theta$
$-x^2=2x^2\cos \theta$
$\cos \theta =-\frac{1}{2}$
$\theta ={120}^{\circ }$
Alternatives:
From triangle law of vector addition, we can observe that all vectors form an equilateral triangle