GramS
\(\small \left\{ o_1 \, := \frac{u1}{\sqrt{u1^{2}}}, \, o_2 \, := \frac{u2 - o_1 \; u2 \; o_1}{\sqrt{\left(u2 - o_1 \; u2 \; o_1 \right)^{2}}}, \, o_3 \, := \frac{u3 - o_2 \; u3 \; o_2 - o_1 \; u3 \; o_1}{\sqrt{\left(u3 - o_2 \; u3 \; o_2 - o_1 \; u3 \; o_1 \right)^{2}}}\right\} \)
Ebene n:=o3 (o1⊗o2)
E:= n (x,y,z) =0,
E: 1 / 3 * x + 2 / 3 * y - 2 / 3 * z = 0
E Hesseform n (x,y,z) = d Abstand
F=Lot (x,y,z)↦ (x,y,z) - d n
\(\small F:= \left(\begin{array}{r}x\\y\\z\\\end{array}\right) - \left( n \cdot \left(\begin{array}{r}x\\y\\z\\\end{array}\right) \right) n \)
u3':=u3 - (n u3) * n =\( \small \left( \begin{array}{r}6 \\ -3 \\ 0 \end{array} \right) \)
Spiegelung an n (x,y,z)=0, |n|=1
u3''=u3 - (2 * u3 n) * n) = \(\small \, \left( \begin{array}{r}5 \\ -5 \\ 2 \end{array} \right)\)
