Trong không gian Oxyz cho hình hộp ABCD.A’B’C’D’. Tìm tọa độ đỉnh A’

* Hướng dẫn giải

Chọn D.

Hình hộp

$$\begin{gathered} ABCD.A\text{'}B\text{'}C\text{'}D\text{'}\Rightarrow \overrightarrow{AD}=\overrightarrow{BC} và \overrightarrow{AA\text{'}}=\overrightarrow{DD\text{'}} \\ \overrightarrow{AD}=\overrightarrow{BC}\iff \left\{\begin{array}{l}{x}_D-x_A=x_C-x_B\\ y_D-y_A=y_C-y_B\\ z_D-z_A=z_C-z_B\end{array}\right.\iff \left\{\begin{array}{l}{x}_D-0=1-1\\ y_D-0=2-0\\ z_D-0=0-0\end{array}\right.\iff \left\{\begin{array}{l}{x}_D=0\\ y_D=2\\ z_D=0\end{array}\right. \\ \overrightarrow{AA\text{'}}=\overrightarrow{DD\text{'}}\iff \iff \left\{\begin{array}{l}{x}_{A\text{'}}-x_A=x_{D\text{'}}-x_D\\ y_{A\text{'}}-y_A=y_{D\text{'}}-y_D\\ z_{A\text{'}}-z_A=z_{D\text{'}}-z_D\end{array}\right.\iff \left\{\begin{array}{l}{x}_{A\text{'}}-0=-1-0\\ y_{A\text{'}}-0=3-2\\ z_{A\text{'}}-0=5-0\end{array}\right.\iff \left\{\begin{array}{l}{x}_{A\text{'}}=-1\\ y_{A\text{'}}=1\\ z_{A\text{'}}=5\end{array}\right. \end{gathered}$$

Vậy $A\text{'}\left(-1;1;5\right).$