1.
a, \(\left\{{}\begin{matrix}x=1+2t\\y=-1-3t\end{matrix}\right.\)
b. \(\overrightarrow{BA}=\left(1;-5\right)\Rightarrow\Delta\) nhận (1;-5) là 1 vtcp
Phương trình tham số: \(\left\{{}\begin{matrix}x=2+t\\y=-4-5t\end{matrix}\right.\)
2.
a. \(4\left(x-5\right)+4\left(y+2\right)=0\Leftrightarrow x+y-3=0\)
b. \(d\left(A;\Delta\right)=\dfrac{\left|2.1+5.6-1\right|}{\sqrt{2^2+5^2}}=\dfrac{31\sqrt{29}}{29}\)
c. \(\overrightarrow{n_{\Delta1}}=\left(1;-1\right)\) ; \(\overrightarrow{n_{\Delta2}}=\left(1;4\right)\)
\(cos\left(\overrightarrow{n_{\Delta1}};\overrightarrow{n_{\Delta2}}\right)=\dfrac{\left|1.1+\left(-1\right).4\right|}{\sqrt{1^2+\left(-1\right)^2}.\sqrt{1^2+4^2}}=\dfrac{3\sqrt{34}}{34}\)
\(\Rightarrow\) Góc giữa 2 đường thẳng xấp xỉ \(59^02'\)
