Đáp án:

•  \(\vec{a} - \vec{b} = (x - 2, 0, 1)\), \(\vec{a} - \vec{c} = (x - 3, -1, 0)\)

•  \(P = |\vec{a} - \vec{b}| + |\vec{a} - \vec{c}| = \sqrt{(x - 2)^2 + 1} + \sqrt{(x - 3)^2 + 1}\)

\(= \sqrt{x^2 - 4x + 5} + \sqrt{x^2 - 6x + 10} = f(x)\)

Thử:  
•  \(x = 2 \quad \Rightarrow \quad f(x) = \sqrt{5} + \sqrt{2} \approx 2.4142\)  
•  \(x = 3 \quad \Rightarrow \quad f(x) = 1 + 2\sqrt{2} \approx 2.4142\)  
•  \(x = \frac{5}{2} \quad \Rightarrow \quad f(x) = \frac{5 + \sqrt{5}}{2} \approx 2.236\)  
•  \(x = \frac{7}{3} \quad \Rightarrow \quad f(x) = \frac{\sqrt{13} + \sqrt{10}}{3} \approx 2.2553\)

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