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Mathematik-Online problems:

Problem 19: Parallelism of and Distance between Planes


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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