Câu 20 : \(P\in\left(Ox\right)\Rightarrow P\left(x;0\right)\)
\(\overrightarrow{MN}=\left(3;-1\right)\)
\(\overrightarrow{MP}=\left(x+2;-2\right)\)
\(M,N,P\) thẳng hàng khi \(\overrightarrow{MN};\overrightarrow{MP}\) cùng phương
\(\Rightarrow\dfrac{x+2}{3}=\dfrac{-2}{-1}\Rightarrow x=4\)
\(\Rightarrow P\left(4;0\right)\Rightarrow\) Chọn D
Câu 21 :
\(\overrightarrow{c}=x.\overrightarrow{a}+y.\overrightarrow{b}\)
\(\Rightarrow\left(2;0\right)=x\left(5;3\right)+y\left(4;2\right)\)
\(\Rightarrow\left\{{}\begin{matrix}5x+4y=2\\3x+2y=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=3\end{matrix}\right.\) \(\Rightarrow\overrightarrow{c}=-2\overrightarrow{a}+3\overrightarrow{b}\Rightarrow\) Chọn B
Câu 22
\(\overrightarrow{AB}=\left(0;-2\right)\overrightarrow{CD}=\left(0;2\right)\Rightarrow\overrightarrow{AB}=-\overrightarrow{CD}\left(1\right)\)
\(\)\(\overrightarrow{AD}=\left(-4;-2\right)\overrightarrow{BC}=\left(-4;-2\right)\Rightarrow\overrightarrow{AD}=\overrightarrow{BC}\left(2\right)\)
\(\left(1\right);\left(2\right)\Rightarrow ABCD\) là hình bình hành (Đúng) (II)
\(\overrightarrow{AC}=\left(-4;-4\right)\Rightarrow\overrightarrow{n_p}=\left(4;-4\right)=4\left(1;-1\right)\)
\(\Rightarrow\left(AC\right):\left(x-2\right)-\left(y-1\right)=0\Rightarrow x-y-1=0\)
\(\overrightarrow{BD}=\left(-4;0\right)\Rightarrow\overrightarrow{n_p}=\left(0;-4\right)=\left(0;-1\right)\)
\(\Rightarrow\left(BD\right):-\left(y+1\right)=0\Rightarrow y=-1\)
Ta thấy \(M\left(0;-1\right)=\left(AC\right)\cap\left(BD\right)\left(Đúng\right)\) (III)
Vậy \(\left(II\right)\&\left(III\right)\) đúng \(\Rightarrow\) Chọn C
