What is the angle between \( \vec{A} \) and the resultant of \( (\o...

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What is the angle between \( \vec{A} \) and the resultant of \( (\overrightarrow{\mathrm{A}}+\hat{\mathrm{B}}) \) and \( (\overrightarrow{\mathrm{A}}-\hat{\mathrm{B}}) \) ?
(1) \( 0^{\circ} \)
(2) \( \tan ^{-1}\left(\frac{A}{B}\right) \)
(3) \( \tan ^{-1}\left(\frac{B}{A}\right) \)
(4) \( \tan ^{-1}\left(\frac{A-B}{A+B}\right) \)
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