Let \( \vec{u} \) and \( \vec{v} \) be unit vectors. If \( \vec{w} \) is a vector such that \( \...

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Let \( \vec{u} \) and \( \vec{v} \) be unit vectors. If \( \vec{w} \) is a vector such that \( \vec{w}+(\vec{w} \times \vec{u})=\vec{v} \), then prove that \( |(\vec{u} \times \vec{v}) \cdot \vec{w}| \leq 1 / 2 \) and that the equality holds if and only if \( \vec{u} \) is perpendicular to \( \vec{v} \).
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