Vector Algebra

For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\vec{A} \cdot(\vec{B} \times \vec{C})=0\), then value of \(x\) is ________.