Đáp án:
\(D\left( {12; - 19} \right).\)
Giải thích các bước giải:
\(\begin{array}{l}
A\left( {2; - 1} \right),\,\,\,B\left( {0;\,\,3} \right),\,\,C\left( {4;\,\,2} \right)\\
Goi\,\,D\left( {a;\,\,b} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\overrightarrow {AD} = \left( {a - 2;\,\,b + 1} \right)\\
\overrightarrow {BD} = \left( {a;\,\,b - 3} \right)\\
\overrightarrow {CD} = \left( {a - 4;\,\,b - 2} \right)
\end{array} \right.\\
\Rightarrow 2\overrightarrow {AD} + 3\overrightarrow {BD} - 4\overrightarrow {CD} = \overrightarrow 0 \\
\Leftrightarrow 2\left( {a - 2;\,\,b + 1} \right) + 3\left( {a;\,\,b - 3} \right) - 4\left( {a - 4;\,\,b - 2} \right) = 0\\
\Leftrightarrow \left\{ \begin{array}{l}
2\left( {a - 2} \right) + 3a - 4\left( {a - 4} \right) = 0\\
2\left( {b + 1} \right) + 3\left( {b - 3} \right) - 4\left( {b - 2} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
a = 12\\
b = - 19
\end{array} \right. \Rightarrow D\left( {12; - 19} \right).
\end{array}\)
