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Zuletzt geändert von Anna Kukin am 2026/05/25 18:19
Von Version 21.1
bearbeitet von Holger Engels
am 2026/04/28 13:07
Änderungskommentar: Neuen Anhang 3 Ebenen schneiden sich in einer Gerade.ggb hochladen
Auf Version 10.1
bearbeitet von Dirk Tebbe
am 2026/04/27 16:18
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

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5 5  [[Kompetenzen.K5]] Ich kann eine Gleichung der Schnittgerade zwischen zwei Ebenen bestimmmen.
6 6  [[Kompetenzen.K5]] [[Kompetenzen.K4]] Ich kann Geraden und Ebenen angeben, die gegebene Lagebeziehungen erfüllen.
7 7  
8 -{{aufgabe id="Aussagen" afb="II" kompetenzen="K1, K6" quelle="Holger Engels" zeit="6"}}
9 -(%class=abc%)
10 -1. Der Richtungsvektor einer Geraden //g// ist als Linearkombination der Spannvektoren der Ebene //E// darstellbar. Erläutere, was sich daraus über die Lage von //g// in Bezug auf //E// sagen lässt.
11 -1. Die Ebenen //E// und //F// teilen sich einen Spannvektor. Erläutere, was sich daraus über die Lage der beiden Ebenen zueinander sagen lässt.
12 -1. Die Ebenen //E// und //F// teilen sich den Punkt //P//. Erläutere, was sich daraus über die Lage der beiden Ebenen zueinander sagen lässt.
8 +{{aufgabe id="Richtungsvektor und Spannvektoren" afb="I" kompetenzen="K1, K6" quelle="Holger Engels" zeit="3"}}
9 +Der Richtungsvektor einer Geraden //g// ist als Linearkombination der Spannvektoren der Ebene //E// darstellbar. Erläutere, was sich daraus über die Lage von //g// in Bezug auf //E// sagen lässt.
13 13  {{/aufgabe}}
14 14  
15 -{{aufgabe id="Schnittgerade" afb="II" kompetenzen="K1, K6" quelle="Martin Stern, Dirk Tebbe" zeit="15"}}
16 -Es sind zwei Ebenen //E// und //F// gegeben durch {{formula}}E: 2x_1-3x_2+x_3=0{{/formula}} und {{formula}}F: 3x_1+2x_2=-1{{/formula}}.
12 +{{aufgabe id="Gemeinsamer Spannvektor" afb="I" kompetenzen="K1, K6" quelle="Holger Engels" zeit="3"}}
13 +Die Ebenen //E// und //F// teilen sich einen Spannvektor. Erläutere, was sich daraus über die Lage der beiden Ebenen zueinander sagen lässt.
14 +{{/aufgabe}}
15 +
16 +{{aufgabe id="Schnittgerade" afb="II" kompetenzen="K1, K6" quelle="Holger Engels" zeit="10"}}
17 +Es sind zwei Ebenen //E// und //F// gegeben:
18 +{{formula}}E: 2x_1-3x_2+x_3=0{{/formula}}
19 +{{formula}}F: 3x_1+2x_2=-1{{/formula}}
17 17  (%class=abc%)
21 +1. Zeige //E// und //F// schneiden sich.
18 18  1. Bestimme die Schnittgerade //g//.
19 -1. Welche besondere Lage haben die beiden Ebenen zueinander?
23 +1. Nimm Stellung zu folgender Aussage:
24 +//Die Projektion von E auf F ergibt g. Die Projektion von F auf E ergibt ebenfalls g//.
20 20  {{/aufgabe}}
21 21  
22 -{{aufgabe id="Lösungsmenge geometrisch" afb="II" kompetenzen="K6" quelle="Frauke Beckstette" zeit="12"}}
23 -Ordne den folgenden linearen Gleichungssystemen jeweils die passende Abbildung zu. Begründe deine Entscheidung.
24 -Visualisiere das verbliebene LGS analog.
25 -(%class="abc horiz"%)
26 -1. (%style="vertical-align: top"%){{formula}}
27 -\begin{aligned}
28 - x_1 + x_2 &= 1 \\
29 - - 3x_2 &= 8 \\
30 - -x_1 + 2x_2 + x_3 &= 4
31 -\end{aligned}
32 -{{/formula}}
33 -1. (%style="vertical-align: top"%){{formula}}
34 -\begin{aligned}
35 - 3x_1 - 2x_2 + x_3 &= 7 \\
36 - -6x_1 + 4x_2 - 2x_3 &= 3 \\
37 - 15x_1 - 10x_2 + 5x_3 &= 5
38 -\end{aligned}
39 -{{/formula}}
40 -1. (%style="vertical-align: top"%){{formula}}
41 -\begin{aligned}
42 - 2x_1 - 2x_2 + 2x_3 &= 2 \\
43 - -2x_1 - 6x_2 + 2x_3 &= 0 \\
44 - 2x_1 + 2x_2 &= 1
45 -\end{aligned}
46 -{{/formula}}
47 -1. (%style="vertical-align: top"%){{formula}}
48 -\begin{aligned}
49 - x_1 + 3x_2 - 2x_3 &= 5 \\
50 - -2x_1 - 6x_2 + 4x_3 &= 1 \\
51 - 2x_1 + x_3 &= 3
52 -\end{aligned}
53 -{{/formula}}
54 -{{/aufgabe}}
27 +
3 Ebenen davon zwei parallel.ggb
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3 Ebenen schneiden sich in einem Punkt.ggb
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3 Ebenen schneiden sich in einem Punkt.svg
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3 Ebenen schneiden sich in einer Gerade.ggb
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