Aufgabe 4

Gegeben sind die Gerade $g:\vec{x}=\left(\begin{array}{c}2\\ 1\\ -1\end{array}\right)+r\cdot \left(\begin{array}{c}1\\ 1\\ -2\end{array}\right),r\in \mathbb{R}\backslash def\backslash arraystretch\{1.25\}\; g:\; \backslash vec\{x\}=\backslash left(\backslash begin\{array\}\{c\}2\; \backslash \backslash \; 1\; \backslash \backslash \; -1\backslash end\{array\}\backslash right)+r\; \backslash cdot\backslash left(\backslash begin\{array\}\{c\}1\; \backslash \backslash \; 1\; \backslash \backslash \; -2\backslash end\{array\}\backslash right),\; r\; \backslash in\; \backslash mathbb\{R\}$ und die Ebene $E:\vec{x}=\left(\begin{array}{c}0\\ 1\\ 4\end{array}\right)+s\cdot \left(\begin{array}{c}4\\ 2\\ 3\end{array}\right)+t\cdot \left(\begin{array}{c}2\\ 0\\ 1\end{array}\right),s,t\in \mathbb{R}\backslash def\backslash arraystretch\{1.25\}\; E:\; \backslash vec\{x\}=\backslash left(\backslash begin\{array\}\{l\}0\; \backslash \backslash \; 1\; \backslash \backslash \; 4\backslash end\{array\}\backslash right)+s\; \backslash cdot\backslash left(\backslash begin\{array\}\{l\}4\; \backslash \backslash \; 2\; \backslash \backslash \; 3\backslash end\{array\}\backslash right)+t\; \backslash cdot\backslash left(\backslash begin\{array\}\{l\}2\; \backslash \backslash \; 0\; \backslash \backslash \; 1\backslash end\{array\}\backslash right),\; \backslash quad\; s,\; t\; \backslash in\; \backslash mathbb\{R\}$.