Ebene in Parameterform aufstellen

Wähle den gemeinsamen Schnittpunkt  $\mathrm{S}\backslash mathrm\; S$  der Geraden als Aufpunkt und die beiden Richtungsvektoren  $\overrightarrow{\mathrm{u}}=\left(\begin{array}{c}2\\ 1\\ -1\end{array}\right)\backslash overrightarrow\{\backslash mathrm\; u\}=\backslash begin\{pmatrix\}2\backslash \backslash 1\backslash \backslash -1\backslash end\{pmatrix\}$  und  $\overrightarrow{\mathrm{v}}=\left(\begin{array}{c}1\\ -2\\ 2\end{array}\right)\backslash overrightarrow\{\backslash mathrm\; v\}=\backslash begin\{pmatrix\}1\backslash \backslash -2\backslash \backslash 2\backslash end\{pmatrix\}$  der Geraden als Richtungsvektoren der Ebene $\mathrm{E}\backslash mathrm\; E$ .

Die Gleichung der Ebene  $\mathrm{E}\backslash mathrm\; E$  lautet dann:     $\mathrm{E}:\overrightarrow{\mathrm{x}}=\left(\begin{array}{c}2\\ 2\\ -3\end{array}\right)+\lambda \cdot \left(\begin{array}{c}2\\ 1\\ -1\end{array}\right)+\mu \cdot \left(\begin{array}{c}1\\ -2\\ 2\end{array}\right)\backslash mathrm\; E:\backslash ;\backslash overrightarrow\{\backslash mathrm\; x\}=\backslash begin\{pmatrix\}2\backslash \backslash 2\backslash \backslash -3\backslash end\{pmatrix\}+\backslash mathrm\backslash lambda\backslash cdot\backslash begin\{pmatrix\}2\backslash \backslash 1\backslash \backslash -1\backslash end\{pmatrix\}+\backslash mathrm\backslash mu\backslash cdot\backslash begin\{pmatrix\}1\backslash \backslash -2\backslash \backslash 2\backslash end\{pmatrix\}$

Veranschaulichung

Ziehe die Grafik mit der rechten Maustaste, um sie zu drehen.