Đáp án:

- \(CH \perp AB \Rightarrow C \in\) mp\(P\) qua  \(H(0, 3, 2), \perp \overrightarrow{AB} = (1, 2, -1)\).  
\(\Rightarrow \text{mp } Q: x + 2y - z - 4 = 0\).  

- \(AC \perp BH \Rightarrow C \in\) mp\(Q\) qua \( A(1, 1, 1), \perp \overrightarrow{BH} = (-2, 0, 2)\).  
\(\Rightarrow \text{mp } Q: -x + z = 0\).  

- \(C \in \text{mp } (ABH): x+z-2=0\) 
\(
\begin{cases}
x + 2y - z = 4 \\  
-x + z = 0  \\ x+z =2
\end{cases}  
\Leftrightarrow 
\begin{cases}
x = 1 \\  
y = 2 \\  
z = 1  
\end{cases}  
\)

Vậy: \(C(1, 2, 1) \Rightarrow \boxed{C} \).