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# Lage von Ebenen

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## Nicolai Schork

on 9 March 2013

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#### Transcript of Lage von Ebenen

Ebene-Ebene Gerade-Ebene schneiden... LGS... www.thesimplemaths.de click! Abo? Gerade schneidet Ebene g E S g: 3
4
7 2
1
-1 + t x = E: 2x1 + 5x2 - x3 = 49 x1=3+2t x2=4+1t x3=7-1t 2(3+2t) +5(4+t) - (7-t) = 49 6+4t + 20+5t -7+t = 49 10t + 19 = 49 t = 3 S(9/7/4) Gerade ist parallel zur Ebene 1.) "Zeilen" der Gerade in E einsetzen g E z.B. 8 = 1 2.) auflösen (z.B. nach t) Gerade liegt in der Ebene E g Zeilen der Gerade in E einsetzen und auflösen z.B. 5 = 5 8 2 Ebenen (KF) schneiden in Gerade E: 3x1 - x2 +2x3 = 7
H: x1 +2x2+3x3 = 14 x3 = t x2 = 5-t x1 = 4-t g: 4
5
0 -1
-1
1 + t x = 2 Ebenen (PF) sind parallel r- 2u - v = -2
s- u - 2v = -3
0 = 2 keine Lösung
-> parallel 1.) Normalvektor vergleichen Punktprobe gleich nur parallel gleiche Richtung ja nein LGS aufstellen
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