Analytical plane geometry

9000090909

Level: 
C
Given lines \(p\) and \(q\), find \(m\in \mathbb{R}\) such that the lines \(p\) and \(q\) are parallel. \[ p\colon 2x+my-3 = 0,\qquad \begin{aligned}[t] q\colon x& = 1 + t, & \\y & = 2 - t;\ t\in \mathbb{R} \\ \end{aligned} \]
\(m = 2\)
\(m = -2\)
\(m = 11\)
\(m = -\frac{1} {11}\)
does not exist

9000090910

Level: 
C
Given lines \(p\) and \(q\), find \(m\in \mathbb{R}\) such that the line \(p\) is parallel to \(q\). \[ p\colon x+4y-3 = 0,\qquad \begin{aligned}[t] q\colon x& = 1 + mt,& \\y & = 2 - 3t;\ t\in \mathbb{R} \\ \end{aligned} \]
\(m = 12\)
\(m = -\frac{1} {12}\)
\(m = 4\)
\(m = \frac{5} {2}\)
\(m = -1\)

9000090902

Level: 
C
Given the parametric line \(p\), find \(m\in \mathbb{R}\) such that the point \(C = [m;3]\) is on the line \(p\). \[ \begin{aligned}p\colon x& = 1 - t, & \\y & = -3 + 2t;\ t\in \mathbb{R} \\ \end{aligned} \]
\(m = -2\)
\(m = 4\)
\(m = 11\)
\(m = -\frac{11} {3} \)
\(m = \frac{3} {2}\)