If \( \vec{a}=\alpha \hat{i}+\beta \hat{j}+3 \hat{k} \) \( \vec{b}=...

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If \( \vec{a}=\alpha \hat{i}+\beta \hat{j}+3 \hat{k} \) \( \vec{b}=-\beta \hat{i}-\alpha \hat{j}-\hat{k} \) and
P \( \vec{c}=\hat{i}-2 \hat{j}-\hat{k} \)

W)
such that \( \vec{a} \cdot \vec{b}=1 \) and \( \vec{b} \cdot \vec{c}=-3 \), then \( \frac{1}{3}((\vec{a} \times \vec{b}) \cdot \vec{c}) \) is equal to
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