Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be three non-zero vectors such that \( \vec{a}+\vec...
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0Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be three non-zero vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \) and \( \lambda \vec{b} \times \vec{a}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}=\overrightarrow{0} \), then find the value of \( \lambda \).
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