If \(\vec A\) and \(\vec B\) are two vectors such that \(\vec A + \vec B\) is perpendicular to \(\vec B\) and \(\vec A+2\vec B\) is perpendicular to \(\vec A\), which of the following is correct?

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**Clarification:** The vectors \(\vec A\) and \(\vec B\) are both non-zero.

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