Câu 11: \(\overrightarrow{u}=3\overrightarrow{a}+2\overrightarrow{b}+4\overrightarrow{c}\)
=>\(\left\{{}\begin{matrix}x_{\overrightarrow{u}}=3\cdot1+2\cdot\left(-3\right)+4\cdot\left(-4\right)=3-6-16=-19\\y_{\overrightarrow{u}}=3\cdot2+2\cdot1+4\cdot2=16\end{matrix}\right.\)
=>Chọn B
Câu 12: A(2;5); B(1;7); C(1;5); D(0;9)
\(\overrightarrow{AB}=\left(1-2;7-5\right)=\left(-1;2\right)\)
\(\overrightarrow{AC}=\left(1-2;5-5\right)=\left(-1;0\right)\)
\(\overrightarrow{AD}=\left(-2;4\right)\)
Vì \(\dfrac{-1}{-2}=\dfrac{2}{4}\)
nên A,B,D thẳng hàng
=>Chọn D
Câu 13: \(AB=\sqrt{\left(4-3\right)^2+\left(-3-0\right)^2}=\sqrt{10}\)
\(BC=\sqrt{\left(8-4\right)^2+\left(-1+3\right)^2}=2\sqrt{5}\)
\(CD=\sqrt{\left(-2-8\right)^2+\left(1+1\right)^2}=2\sqrt{26}\)
\(AC=\sqrt{\left(8-3\right)^2+\left(-1-0\right)^2}=\sqrt{5^2+1^2}=\sqrt{26}\)
\(AD=\sqrt{\left(-2-3\right)^2+\left(1-0\right)^2}=\sqrt{26}\)
Vì AC+AD=CD
nên C,A,D thẳng hàng
=>Chọn D
Câu 14:
A(-2m;-m); B(2m;m); O(0;0)
Để đường thẳng AB đi qua O thì A,B,O thẳng hàng
\(\overrightarrow{AB}=\left(4m;2m\right);\overrightarrow{AO}=\left(2m;m\right)\)
Để A,B,O thẳng hàng thì \(\dfrac{4m}{2m}=\dfrac{2m}{m}\)
=>2=2(đúng)
=>Chọn C
