Question
Two vectors $\vec A\,{\rm{ and }}\vec B$ are such that $\vec A + \vec B = \vec A - \vec B$. Then
$(\vec{A}-\vec{A})+\vec{B}+\vec{B}=0$
$0+2\vec{B}=0$
$\vec{B}=0$
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Reason $(R):$ Power factor of series $R-L$ circuit is given by $\cos \theta=\frac{2 R }{\sqrt{ R ^2+\omega^2 L ^2}}$

