9000101004

SubArea: 
Analytic geometry in a space
Level: 
A
Project ID: 
9000101004
Source Problem: 
2010005003
Accepted: 
1
Clonable: 
1
Easy: 
0
Find all the values of the real parameter \(m\) so that the lines \(p\) and \(q\) are skew lines. \[ \begin{aligned}p\colon x& = 1 + t, & \\y & = 2 - t, \\z & = 1 - t;\ t\in \mathbb{R} \\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = s, & \\y & = 1 + s, \\z & = 3 + ms;\ s\in \mathbb{R} \\ \end{aligned} \]
\(m\in\mathbb{R}\setminus\{-2\}\)
No solution exists.
The lines are skew for every real \(m\).
\(m = -2\)