If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are unit vectors such t...

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If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are unit vectors such that
\( \mathrm{P} \)
W \( \vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0} \), then \( |\vec{a} \times \vec{c}| \) is equal to:
(1) \( \frac{\sqrt{15}}{4} \)
(2) \( \frac{1}{4} \)
(3) \( \frac{15}{16} \)
(4) \( \frac{\sqrt{15}}{16} \)
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