Đáp án: 

• \(\begin{cases}
\overrightarrow{AB} = (-3, -1, 1)\\
\overrightarrow{AC} = (4, 1, 2)
\end{cases}
\Rightarrow[\overrightarrow{AB}, \overrightarrow{AC}] = (-3, 10, 1)\)

\(\overrightarrow{AM} = (1, 0, m + 2)\)

• \(
[\overrightarrow{AB}, \overrightarrow{AC}]. \overrightarrow{AM} = -3+ m + 2 = 0
 \Leftrightarrow m = 1\)

\(\Rightarrow\) Vậy chọn \(\boxed{\text{C}} \)