Two vectors \( \vec{A} \) and \( \vec{B} \) are such that \( \vec{A}+\vec{B}=\vec{C} \) and \( A...

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Two vectors \( \vec{A} \) and \( \vec{B} \) are such that \( \vec{A}+\vec{B}=\vec{C} \) and \( A^{2}+B^{2}=C^{2} \). Which of the following statements, is correct?
(1) \( \vec{A} \) is parallel to \( \vec{B} \)
(2) \( \vec{A} \) is anti-parallel to \( \vec{B} \)
(3) \( \vec{A} \) is perpendicular to \( \vec{B} \)
(4) \( \vec{A} \) and \( \overrightarrow{\mathrm{B}} \) are equal in magnitude
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