Let \( \vec{a}=6\hat{i}+9\hat{j}+12\hat{k},\; \vec{b}=\alpha \hat{i}+11\hat{j}-2\hat{k} \) and \( \vec{c} \) be vectors such that \( \vec{a}\times\vec{c}=\vec{a}\times\vec{b} \). If \( \vec{a}\cdot\vec{c}=-12, \; \vec{c}\cdot(\hat{i}-2\hat{j}+\hat{k})=5 \), then \( \vec{c}\cdot(\hat{i}+\hat{j}+\hat{k}) \) is equal to ________.
