Value of the scalar triple product \(\vec{a}\cdot(\vec{b}\times\vec{c})\) is (answer in integer) ______.
\[ \vec{a}=2\hat{i}-3\hat{j}+4\hat{k} \]
\[ \vec{b}=\hat{i}+2\hat{j}-3\hat{k} \]
\[ \vec{c}=3\hat{i}+4\hat{j}-\hat{k} \]
Here, \(\hat{i}\), \(\hat{j}\) and \(\hat{k}\) are mutually orthogonal unit vectors.