Google
Câu hỏi: Trong không gian $\text{Ox}yz$ cho hình hộp $ABC\text{D}.{A}'{B}'{C}'\text{{D}'}$ biết $A\left( 1,0,1 \right)$, $B\left( 2,1,2 \right)$, $D\left( 1,-1,1 \right)$, ${C}'\left( 4,5,-5 \right)$. Tọa độ ${A}'$ lả
A. ${A}'\left( 4,6,-5 \right)$.
B. ${A}'\left( -3,4,-1 \right)$.
C. ${A}'\left( 3,5,-6 \right)$.
D. ${A}'\left( 3,5,6 \right)$.
Gọi $C\left( x,y,z \right)$. $\overrightarrow{A\text{D}}=\left( 0,-1,0 \right)$ ; $\overrightarrow{BC}=\left( x-2,y-1,z-2 \right)$.
Ta có $\overrightarrow{A\text{D}}=\overrightarrow{BC}$ $\Leftrightarrow \left\{ \begin{aligned}
& x-2=0 \\
& y-1=-1 \\
& z-2=0 \\
\end{aligned} \right.\Rightarrow C\left( 2,0,2 \right) $.Do đó $ \overrightarrow{AC}=\left( 1,0,1 \right)$.
Gọi ${A}'\left( a,b,c \right)$ ; $\overrightarrow{{A}'{C}'}=\left( 4-a,5-b,-5-c \right)$ ; mà $\overrightarrow{AC}=\overrightarrow{{A}'{C}'}\Leftrightarrow \left\{ \begin{aligned}
& 4-a=1 \\
& 5-b=0 \\
& -5-c=1 \\
\end{aligned} \right.\Rightarrow {A}'\left( 3,5,-6 \right)$.
A. ${A}'\left( 4,6,-5 \right)$.
B. ${A}'\left( -3,4,-1 \right)$.
C. ${A}'\left( 3,5,-6 \right)$.
D. ${A}'\left( 3,5,6 \right)$.
Gọi $C\left( x,y,z \right)$. $\overrightarrow{A\text{D}}=\left( 0,-1,0 \right)$ ; $\overrightarrow{BC}=\left( x-2,y-1,z-2 \right)$.
Ta có $\overrightarrow{A\text{D}}=\overrightarrow{BC}$ $\Leftrightarrow \left\{ \begin{aligned}
& x-2=0 \\
& y-1=-1 \\
& z-2=0 \\
\end{aligned} \right.\Rightarrow C\left( 2,0,2 \right) $.Do đó $ \overrightarrow{AC}=\left( 1,0,1 \right)$.
Gọi ${A}'\left( a,b,c \right)$ ; $\overrightarrow{{A}'{C}'}=\left( 4-a,5-b,-5-c \right)$ ; mà $\overrightarrow{AC}=\overrightarrow{{A}'{C}'}\Leftrightarrow \left\{ \begin{aligned}
& 4-a=1 \\
& 5-b=0 \\
& -5-c=1 \\
\end{aligned} \right.\Rightarrow {A}'\left( 3,5,-6 \right)$.
Đáp án A.