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Câu hỏi: Trong hệ tọa độ $Oxyz,$ cho ba vectơ $\overrightarrow{a}=\overrightarrow{i}+2\overrightarrow{j}-3\overrightarrow{k},\overrightarrow{b}=-3\overrightarrow{j}+4\overrightarrow{k},\overrightarrow{c}=-\overrightarrow{i}-2\overrightarrow{j}.$ Khẳng định nào sau đây là đúng?
A. $\overrightarrow{a}=\left( 1;2;-3 \right),\overrightarrow{b}=\left( 0;-3;4 \right),\overrightarrow{c}=\left( -1;-2;0 \right).$
B. $\overrightarrow{a}=\left( 1;2;3 \right),\overrightarrow{b}=\left( 0;3;4 \right),\overrightarrow{c}=\left( -1;-2;0 \right).$
C. $\overrightarrow{a}=\left( 1;2;3 \right),\overrightarrow{b}=\left( 0;-3;4 \right),\overrightarrow{c}=\left( -1;2;0 \right).$
D. $\overrightarrow{a}=\left( 1;2;-3 \right),\overrightarrow{b}=\left( -3;4;0 \right),\overrightarrow{c}=\left( -1;0;-2 \right).$
A. $\overrightarrow{a}=\left( 1;2;-3 \right),\overrightarrow{b}=\left( 0;-3;4 \right),\overrightarrow{c}=\left( -1;-2;0 \right).$
B. $\overrightarrow{a}=\left( 1;2;3 \right),\overrightarrow{b}=\left( 0;3;4 \right),\overrightarrow{c}=\left( -1;-2;0 \right).$
C. $\overrightarrow{a}=\left( 1;2;3 \right),\overrightarrow{b}=\left( 0;-3;4 \right),\overrightarrow{c}=\left( -1;2;0 \right).$
D. $\overrightarrow{a}=\left( 1;2;-3 \right),\overrightarrow{b}=\left( -3;4;0 \right),\overrightarrow{c}=\left( -1;0;-2 \right).$
Phương pháp:
Sử dụng tọa độ của 1 vectơ: $\overrightarrow{u}=\left( x;y;z \right)\Leftrightarrow \overrightarrow{u}=x\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}.$
Cách giải:Ta có: $\overrightarrow{a}=\overrightarrow{i}+2\overrightarrow{j}-3\overrightarrow{k},\overrightarrow{b}=-3\overrightarrow{j}+4\overrightarrow{k},\overrightarrow{c}=-\overrightarrow{i}-2\overrightarrow{j}\Rightarrow \left\{ \begin{aligned}
& \overrightarrow{a}=\left( 1;2;-3 \right) \\
& \overrightarrow{b}=\left( 0;-3;4 \right) \\
& \overrightarrow{c}=\left( -1;-2;0 \right) \\
\end{aligned} \right.$
Sử dụng tọa độ của 1 vectơ: $\overrightarrow{u}=\left( x;y;z \right)\Leftrightarrow \overrightarrow{u}=x\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}.$
Cách giải:Ta có: $\overrightarrow{a}=\overrightarrow{i}+2\overrightarrow{j}-3\overrightarrow{k},\overrightarrow{b}=-3\overrightarrow{j}+4\overrightarrow{k},\overrightarrow{c}=-\overrightarrow{i}-2\overrightarrow{j}\Rightarrow \left\{ \begin{aligned}
& \overrightarrow{a}=\left( 1;2;-3 \right) \\
& \overrightarrow{b}=\left( 0;-3;4 \right) \\
& \overrightarrow{c}=\left( -1;-2;0 \right) \\
\end{aligned} \right.$
Đáp án A.