Question

Two equal vectors have a resultant equal to either of them, then the angle between them will be

• A. $120°$
• B. $110°$
• C. $60°$
• D. $150°$

Answer 1

The correct option is A

$120°$

Find the required angle:

Let the two vectors be $A$ and $B$ and both at an angle of $\theta$ from each other with a resultant $R$

From the triangle law of vector addition,

$R^2=A^2+B^2+2AB\cos \theta$

Now, $A=B=R$ [given]

$$\begin{gathered} \Rightarrow A^2=A^2+A^2+2A^2\cos \theta \\ \Rightarrow A^2=2A^2(1+\cos \theta ) \\ \Rightarrow \cos \theta =\frac{-1}{2} \\ \Rightarrow \theta =120° \end{gathered}$$

Hence, the correct option is (A).