Trong không gian Oxyz cho ba điểm A(1;1;1), B(5;-1;2), C(3;2;-4). Tìm tọa độ

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Trong không gian Oxyz cho ba điểm \({\rm{A}}\left( {1\,;\,\,1\,;\,\,1} \right),\,\,{\rm{B}}\left( {5\,;\,\, - 1\,;\,\,2} \right),\,\,{\rm{C}}\left( {3\,;\,\,2\,;\,\, - 4} \right)\). Tìm tọa độ điểm \[M\] thỏa mãn \(\overrightarrow {{\rm{MA}}} + 2\overrightarrow {{\rm{MB}}} - \overrightarrow {{\rm{MC}}} = \vec 0\).

\({\rm{M}}\left( {4\,;\,\, - \frac{3}{2}\,;\,\,\frac{9}{2}} \right)\).

\({\rm{M}}\left( {4\,;\,\, - \frac{3}{2}\,;\,\, - \frac{9}{2}} \right)\).

\({\rm{M}}\left( {4\,;\,\,\frac{3}{2}\,;\,\,\frac{9}{2}} \right)\).

\(M\left( { - \,4\,;\,\, - \frac{3}{2}\,;\,\,\frac{9}{2}} \right)\).

Giải thích

Gọi \(M\left( {x\,;\,\,y\,;\,\,z} \right)\). Ta có \(\overrightarrow {{\rm{MA}}} + 2\overrightarrow {{\rm{MB}}} - \overrightarrow {{\rm{MC}}} = \vec 0\)

\[ \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{1 - {\rm{x}} + 2\left( {5 - {\rm{x}}} \right) - \left( {3 - {\rm{x}}} \right) = 0}\\{1 - {\rm{y}} + 2\left( { - 1 - {\rm{y}}} \right) - \left( {2 - {\rm{y}}} \right) = 0}\\{1 - {\rm{z}} + 2\left( {2 - {\rm{z}}} \right) - \left( { - 4 - {\rm{z}}} \right) = 0}\end{array} \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{{\rm{x}} = 4}\\{{\rm{y}} = - \frac{3}{2} \Leftrightarrow {\rm{M}}\left( {4\,;\,\, - \frac{3}{2}\,;\,\,\frac{9}{2}} \right).{\rm{ }}}\\{{\rm{z}} = \frac{9}{2}}\end{array}} \right.} \right.\]Chọn A.