Let \( \vec{a}=\hat{i}+\hat{j}+\hat{k} \) and \( \vec{b}=\hat{j}-\hat{k} \). If \( \vec{c} \) is a vector such that \( \vec{a}\times \vec{c}=-\vec{b} \) and \( \vec{a}\cdot \vec{c}=3 \), then \( \vec{a}\cdot (\vec{b}\times \vec{c}) \) is equal to:
\( -6 \)
\( 2 \)
\( -2 \)
\( 6 \)
