If \( \vec{x} \) and \( \vec{y} \) be two non-zero vectors such tha...

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If \( \vec{x} \) and \( \vec{y} \) be two non-zero vectors such that
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W \( |\vec{x}+\vec{y}|=|\vec{x}| \) and \( 2 \vec{x}+\lambda \vec{y} \) is perpendicular to \( \vec{y} \), then the value of \( \lambda \) is
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