=for timestamp
Di Feb 21 17:22:57 CET 2006

=head2 56. Hausaufgabe

=head3 Angabe einer bestimmten Strecke

M<A(5,3,4); \quad B(-10, -3, -8);>

M<\begin{array}{rcl}
{} \left[AB\right] &=&
{}   \left\{
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} \middle|
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} =
{}     \begin{pmatrix}5\\3\\4\end{pmatrix} +
{}     k \begin{pmatrix}-10 - 5\\-3 - 3\\-8 - 4\end{pmatrix}
{}     \text{mit } k \in \left[0, 1\right]
{}   \right\} = \vspace*{0.8em}\\
{} &=&
{}   \left\{
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} \middle|
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} =
{}     \begin{pmatrix}-10\\-3\\-8\end{pmatrix} +
{}     k \begin{pmatrix}5 - \left(-10\right)\\3 - \left(-3\right)\\4 - \left(-8\right)\end{pmatrix}
{}     \text{mit } k \in \left[0, 1\right]
{}   \right\} = \vspace*{0.8em}\\
{} &=&
{}   \left\{
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} \middle|
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} =
{}     \vec A + k \overrightarrow{AB}
{}     \text{ mit } k \in \left[0, 1\right]
{}   \right\} = \vspace*{0.8em}\\
{} &=&
{}   \left\{
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} \middle|
{}     \begin{pmatrix}q_1\\q_2\\q_3\end{pmatrix} =
{}     \vec B + k \overrightarrow{BA}
{}     \text{ mit } k \in \left[0, 1\right]
{}   \right\}\!;
\end{array}>