Lösung Quadrat begründen

Version 3.1 von Daniel Stocker am 2024/02/05 16:38

$\overrightarrow{AB} = \left(\begin{array}{c} 1-5 \\ 1-(-1) \\ -1-3\end{array}\right) = \left(\begin{array}{c} -4 \\ 2 \\ -4\end{array}\right)$

$\overrightarrow{BC} = \left(\begin{array}{c} -1-1 \\ 5-1 \\ 3-(-1)\end{array}\right) = \left(\begin{array}{c} -2 \\ 4 \\ 4\end{array}\right)$

$\overrightarrow{CD} = \left(\begin{array}{c} 3-(-1) \\ 3-5 \\ 7-3\end{array}\right) = \left(\begin{array}{c} 4 \\ -2 \\ 4\end{array}\right)$

$\overrightarrow{DA} = \left(\begin{array}{c} 5-3 \\ -1-3 \\ 3-7\end{array}\right) = \left(\begin{array}{c} 2 \\ -4 \\ -4\end{array}\right)$

$\Rightarrow \overrightarrow{AB} = - \overrightarrow{CD} \text{ und } \overrightarrow{BC} = - \overrightarrow{DA}$