Stellen Sie E in Normalform dar.

Question

Die Ebene \( E \subseteq \mathbb{R}^{3} \) sei definiert durch
$$ E=\left\{\left(\begin{array}{c} {4} \\ {-3} \\ {-1} \end{array}\right)+\lambda\left(\begin{array}{c} {2} \\ {-5} \\ {2} \end{array}\right)+\mu\left(\begin{array}{c} {-1} \\ {2} \\ {-3} \end{array}\right) | \lambda, \mu \in \mathbb{R}\right\} $$
Stellen Sie \( E \) in Hesse-Normalform dar.

Answer 1

n = [2, -5, 2] ⨯ [-1, 2, -3] = [11, 4, -1]

|n| = |[11, 4, -1]| = √138

E: (X - [4, -3, -1]) · [11, 4, -1]/√138 = 0