\(\left\{{}\begin{matrix}x=1-2t\\y=3+t\end{matrix}\right.\)\(\Rightarrow\overrightarrow{u}=\left(-2;1\right)\Rightarrow\overrightarrow{n}=\left(-1;-2\right)\)
\(\Rightarrow pt\) \(\Delta:-1\left(x-1\right)-2\left(y-3\right)=0\)
\(\Leftrightarrow-x+1-2y+6=0\Leftrightarrow-x-2y+7=0\Leftrightarrow y=\dfrac{-x}{2}+\dfrac{7}{2}\)
\(M\in\Delta\Rightarrow M=\left(x;-\dfrac{x}{2}+\dfrac{7}{2}\right)\)
\(\Rightarrow\overrightarrow{MA}=\left(1-x;\dfrac{x-3}{2}\right)\)
\(\Rightarrow\overrightarrow{MB}=\left(3-x;\dfrac{x-7}{2}\right);\Rightarrow\overrightarrow{MC}=\left(1-x;\dfrac{x-9}{2}\right)\)
\(\Rightarrow\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}=\left(5-3x;\dfrac{3x-19}{2}\right)\)
\(\Rightarrow\left|\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}\right|=\sqrt{\left(5-3x\right)^2+\left(\dfrac{3x-19}{2}\right)^2}=\sqrt{9x^2-30x+25+\dfrac{9x^2-114x+361}{4}}=\dfrac{\sqrt{36x^2-120x+100+9x^2-114x+361}}{2}=\dfrac{\sqrt{45x^2-264x+461}}{2}=\dfrac{\sqrt{45\left(x-\dfrac{44}{15}\right)^2+\dfrac{369}{5}}}{2}\ge\dfrac{\sqrt{\dfrac{365}{5}}}{2}=\dfrac{\sqrt{73}}{2}\Rightarrow min\Leftrightarrow x=\dfrac{44}{15}\Rightarrow M=\left(\dfrac{44}{15};\dfrac{61}{30}\right)\)
\(ktra\) \(tính\) \(toán\) \(lại\) \(giùm\)
