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 $\_\_\_\_$