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If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\pi / 3$, then $\vec{a}$ is equal to
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The correct answer is:
$\pm \frac{2}{\sqrt{3}}(\vec{b} \times \vec{c})$
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