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 ${120}^o$

According to the question magnitude of the resultant of the two vectors is equal to the magnitude of the either vectors.

So,

Let $\overrightarrow{A}$ and $\overrightarrow{B}$ be given two vectors.

We can write,
$|\overrightarrow{A}|=|\overrightarrow{B}|=|\overrightarrow{R}|$ = x(say)

We know that the magnitude of the vecors is given as
$R=\sqrt{A^2+B^2+2AB\cos \theta }$

Or,
$x^2=x^2+x^2+2x^2\cos \theta$

Or,
$-x^2=2x^2\cos \theta$

After solving
$\cos \theta =-\frac{1}{2}$

Therefore,
$\theta ={120}^{\circ }$
Hence the angle between the two vectors is $\theta ={120}^0$