Trong mặt phẳng \(O x y z\), cho ba điểm \(A(1 ; 2 ; 0), B(2 ; 1 ; 2), C(-1 ; 3 ; 1)\).
Xác định tọa độ điểm M thỏa mãn \(\overrightarrow{M A}+2 \overrightarrow{M B}-\overrightarrow{M C}=\overrightarrow{0}\).
\(M\left(3 ; 1 ; \frac{3}{2}\right)\).
\(M\left(3 ; \frac{1}{2} ; \frac{3}{2}\right)\).
\(M\left(3 ; \frac{1}{2} ; 0\right)\).
\(M\left(\frac{-1}{2} ; \frac{1}{2} ; \frac{3}{2}\right)\).
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Gọi \(M(x ; y ; z)\)
Ta có: \(\overrightarrow{M A}+2 \overrightarrow{M B}-\overrightarrow{M C}=\overrightarrow{0} \Rightarrow 2 \overrightarrow{M B}+\overrightarrow{C A}=\overrightarrow{0} \Rightarrow 2 \overrightarrow{M B}=\overrightarrow{A C} \Rightarrow \overrightarrow{M B}=\frac{1}{2} \overrightarrow{A C}\)
Suy ra \(\left\{\begin{array}{l}2-x=\frac{1}{2}(-1-1) \\ 1-y=\frac{1}{2}(3-2) \\ 2-z=\frac{1}{2}(1-0)\end{array} \Leftrightarrow\left\{\begin{array}{l}x=3 \\ y=\frac{1}{2} \\ z=\frac{3}{2}\end{array} \Rightarrow M\left(3 ; \frac{1}{2} ; \frac{3}{2}\right)\right.\right.\).
Câu hỏi liên quan
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