Cho hình hộp chữ nhật ABCD.A'B'...

A

- Hướng dẫn giải

Đáp án A

Chọn hệ trục tọa độ như hình vẽ

A'(0;0;0), B'(4a;0;0), C'(4a;4a;0), M'(0;2a;2a)

$$\begin{gathered} \overrightarrow{A\text{'}B\text{'}}\left(4a;0;0\right), \overrightarrow{C\text{'}M}\left(-4a;-2a;2a\right)\Rightarrow \left[\overrightarrow{A\text{'}B\text{'}}, \overrightarrow{C\text{'}M}\right]=\left(0;-8a^2;-8a^2\right) \\ \overrightarrow{A\text{'}M}\left(0;2a;2a\right) \\ d(A\text{'}B\text{'}, C\text{'}M)=\frac{\left[\left[\overrightarrow{A\text{'}B\text{'}}, \overrightarrow{C\text{'}M}\right]A\text{'}M\right]}{\left[\overrightarrow{A\text{'}B\text{'}}, \overrightarrow{C\text{'}M}\right]}=\frac{32a^3}{8\sqrt{2}{a}^2}=2\sqrt{2}a \end{gathered}$$