Level:
Project ID:
2010005003
Source Problem:
Accepted:
0
Clonable:
1
Easy:
0
Find all the values of the real parameter \(p\)
so that the lines \(a\)
and \(b\)
are skew lines.
\[
\begin{aligned}a\colon x& =- 1 + 2m, &
\\y & = 1 - pm,
\\z & = 2 - m;\ m\in \mathbb{R}
\\ \end{aligned}\qquad \qquad \begin{aligned}b\colon x& = 3+2n, &
\\y & = 1-n,
\\z & = 5+4n;\ n\in \mathbb{R}
\\ \end{aligned}
\]
\(p\in\mathbb{R}\setminus\{-1\}\)
\(p = -1\)
No solution exists.
The lines are skew for every real \(p\).