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\(\left\{{}\begin{matrix}\overrightarrow{PM}=\left(-1-a;2-b\right)\\3\overrightarrow{PN}=3\left(1-a;-b\right)=\left(3-3a;-3b\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-1-a=3-3a\\2-b=-3b\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=2\\b=1\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
(1); vecto u=2*vecto a-vecto b
=>\(\left\{{}\begin{matrix}x=2\cdot1-0=2\\y=2\cdot\left(-4\right)-2=-10\end{matrix}\right.\)
(2): vecto u=-2*vecto a+vecto b
=>\(\left\{{}\begin{matrix}x=-2\cdot\left(-7\right)+4=18\\y=-2\cdot3+1=-5\end{matrix}\right.\)
(3): vecto a=2*vecto u-5*vecto v
\(\Leftrightarrow\left\{{}\begin{matrix}a=2\cdot\left(-5\right)-5\cdot0=-10\\b=2\cdot4-5\cdot\left(-3\right)=15+8=23\end{matrix}\right.\)
(4): vecto OM=(x;y)
2 vecto OA-5 vecto OB=(-18;37)
=>x=-18; y=37
=>x+y=19
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\overrightarrow {AB} = \left( {{x_B} - {x_A};{y_B} - {y_A}} \right) = \left( { - 1;1} \right)\)
Chọn C.
\(\overrightarrow{AB}=\left(-1;-4\right)\) ; \(\overrightarrow{AC}=\left(1;-2\right)\)
\(\Rightarrow3\overrightarrow{AB}-2\overrightarrow{AC}=\left(-5;-8\right)\)
Gọi \(E\left(x;y\right)\Rightarrow\overrightarrow{AE}=\left(x-2;y-5\right)\)
\(\Rightarrow\left\{{}\begin{matrix}x-2=-5\\y-5=-8\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-3\\y=-3\end{matrix}\right.\) \(\Rightarrow A\left(-3;-3\right)\)