Let \( \vec{a}=3\hat{i}+\hat{j}-2\hat{k},\; \vec{b}=4\hat{i}+\hat{j}+7\hat{k} \) and \( \vec{c}=\hat{i}-3\hat{j}+4\hat{k} \) be three vectors. If a vectors \( \vec{p} \) satisfies \( \vec{p}\times\vec{b}=\vec{c}\times\vec{b} \) and \( \vec{p}\cdot \vec{a}=0 \), then \( \vec{p}\cdot(\hat{i}-\hat{j}-\hat{k}) \) is equal to:
