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The angle between two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$ . Resultant of these two vectors is $\overrightarrow{R}$ Which makes an angle of $\large\frac{\theta}{2}$ with $\overrightarrow{A}$. Which of the following is true?

$\begin{array}{1 1}(A)\;A=2B \\(B)\;A=B \\(C)\;B=2A\\(D)\;A= 1/B \end{array}$

$\tan \large\frac{\theta}{2}=\frac{B \sin \theta}{A+B \cos \theta} = \large\frac{2B \sin \theta/2 \cos \theta/2}{A+B ( 2 \cos \theta/2 -1)}$
Solving this we get,
$A=B$
Hence B is the correct answer.

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