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Mathematik-Online problems:

Problem 19: Parallelism of and Distance between Planes

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Given the planes

$\displaystyle E_1: x=\left(\begin{array}{r}1\\ 8\\ -1\end{array}\right)+s\left(... ...ft(\begin{array}{c}3\\ 1\\ 0\end{array}\right) \quad {\mbox{\normalsize {and}}}$

$\displaystyle E_2(\alpha): x=\left(\begin{array}{r}6\\ -13\\ 19\end{array}\righ... ... 2\end{array}\right)+v\left(\begin{array}{r}-2\\ -1\\ \alpha\end{array}\right) $


in $ \mathbb{R}^3$ , with $ s, t, u, v, \alpha\in\mathbb{R}$ . For which $ \alpha$ the planes are parallel? Find for these $ \alpha$ the distance between $ E_1$ and $ E_2(\alpha)$ .

(Authors: Kimmerle/Roggenkamp/Höfert)

Solution:

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  automatisch erstellt am 9.  5. 2008