Geraden Schnittpunktbestimmung

$$\begin{array}{rl}g:\vec{x}& =\left(\begin{array}{c}2\\ 1\\ -2\end{array}\right)+\lambda \left(\begin{array}{c}2\\ 3\\ 1\end{array}\right)\\ h:\vec{x}& =\left(\begin{array}{c}4\\ 3\\ 1\end{array}\right)+\lambda \left(\begin{array}{c}4\\ 2\\ 5\end{array}\right)\end{array}$$

Schnittpunktbestimmung:

$$\begin{array}{rl}\left(\begin{array}{c}2\\ 1\\ -2\end{array}\right)+\lambda \left(\begin{array}{c}2\\ 3\\ 1\end{array}\right)& =\left(\begin{array}{c}4\\ 3\\ 1\end{array}\right)+\mu \left(\begin{array}{c}4\\ 2\\ 5\end{array}\right)|-\mu \left(\begin{array}{c}4\\ 2\\ 5\end{array}\right)-\left(\begin{array}{c}2\\ 1\\ -2\end{array}\right)\\ -\mu \left(\begin{array}{c}4\\ 2\\ 5\end{array}\right)+\lambda \left(\begin{array}{c}2\\ 3\\ 1\end{array}\right)& =\left(\begin{array}{c}2\\ 2\\ 3\end{array}\right)\\ \left[\begin{array}{ccc}-4& 2& 2\\ -2& 3& 2\\ -5& 1& 3\end{array}\right]& \to \text{rref}\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\to \left|\begin{array}{c}\lambda =0\\ \mu =0\\ 0=1\end{array}\right|\begin{array}{c}\\ \to \text{Es gibt keinen Schnittpunkt}\\ \to \text{g und h sind windschief}\end{array}\end{array}$$