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Câu hỏi: Trong không gian $Oxyz$, cho các vectơ $\overrightarrow{a}=2\overrightarrow{i}-3\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{b}=-2\overrightarrow{i}+\overrightarrow{j}+2\overrightarrow{k}$. Tọa độ của vectơ $\overrightarrow{u}=2\overrightarrow{a}+\overrightarrow{b}$ là
A. $\overrightarrow{u}=\left( 2;-7;4 \right)$.
B. $\overrightarrow{u}=\left( 0;-4;6 \right)$.
C. $\overrightarrow{u}=\left( 2;-5;4 \right)$.
D. $\overrightarrow{u}=\left( 6;-7;0 \right)$.
A. $\overrightarrow{u}=\left( 2;-7;4 \right)$.
B. $\overrightarrow{u}=\left( 0;-4;6 \right)$.
C. $\overrightarrow{u}=\left( 2;-5;4 \right)$.
D. $\overrightarrow{u}=\left( 6;-7;0 \right)$.
Ta có $\overrightarrow{a}=2\overrightarrow{i}-3\overrightarrow{j}+\overrightarrow{k}, \overrightarrow{b}=-2\overrightarrow{i}+\overrightarrow{j}+2\overrightarrow{k}\Rightarrow \overrightarrow{a}=\left( 2; -3; 1 \right), \overrightarrow{b}=\left( -2; 1; 2 \right)$.
Suy ra $\overrightarrow{u}=2\overrightarrow{a}+\overrightarrow{b}=\left( 2;-5;4 \right)$.
Suy ra $\overrightarrow{u}=2\overrightarrow{a}+\overrightarrow{b}=\left( 2;-5;4 \right)$.
Đáp án C.