Cho hình hộp chữ nhật ABCD.A’B’C’D...

A

- Hướng dẫn giải

Đáp án A

Giả sử AB = x

$\begin{array}{l}B\text{'}(0;0;0),A\text{'}(x;0;0),C\text{'}(0;4a;0),M(x;2a;2a)\\ \overrightarrow{A\text{'}B\text{'}}(x;0;0),\overrightarrow{C\text{'}M}(x;-2a;2a),\overrightarrow{B\text{'}C\text{'}}(0;4a;0)\\ \text{[}\overrightarrow{A\text{'}B\text{'}},\overrightarrow{C\text{'}M}\text{]}=(0;-2ax;-2ax)\\ d(A\text{'}B\text{'};C\text{'}M)=\frac{\left|\text{[}\overrightarrow{A\text{'}B\text{'}},\overrightarrow{C\text{'}M}\text{]}\overrightarrow{B\text{'}C\text{'}}\right|}{\left|\text{[}\overrightarrow{A\text{'}B\text{'}},\overrightarrow{C\text{'}M}\text{]}\right|}\\ =\frac{\left|-8a^{2}x\right|}{\sqrt{8a^2{x}^2}}=2\sqrt{2}a\end{array}$