Consider the vectors \(\vec{A}=\hat{i}+\hat{j}-\hat{k}, \vec{B}=2 \hat{i}-\hat{j}+\hat{k}, \vec{C}=\frac{1}{\sqrt{5}}(\hat{i}-2 \hat{j}+2 \hat{k})\). What is the value of \(\vec{C} \cdot(\vec{A} \times \vec{B}) ?\)
(A) 1
(B) 0
(C) \(3 \sqrt{2}\)
(D) \(18 \sqrt{5}\)