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Zuletzt geändert von Martin Rathgeb am 2026/07/07 10:20
Von Version 11.1
bearbeitet von Holger Engels
am 2026/04/27 17:03
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 26.1
bearbeitet von Holger Engels
am 2026/04/28 13:10
Änderungskommentar: Anhang 3 Ebenen schneiden sich in einem Punkt.svg verschoben nach 3 Ebenen A.svg.

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13 13  {{/aufgabe}}
14 14  
15 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:
17 -{{formula}}E: 2x_1-3x_2+x_3=0{{/formula}}
18 -{{formula}}F: 3x_1+2x_2=-1{{/formula}}
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}}.
19 19  (%class=abc%)
20 -1. Zeige //E// und //F// schneiden sich.
21 21  1. Bestimme die Schnittgerade //g//.
22 -1. Nimm Stellung zu folgender Aussage:
23 -//Die Projektion von E auf F ergibt g. Die Projektion von F auf E ergibt ebenfalls g//.
19 +1. Welche besondere Lage haben die beiden Ebenen zueinander?
24 24  {{/aufgabe}}
25 25  
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}}
26 26  
55 +[[image:3 Ebenen A.svg||width=300]][[image:3 Ebenen B.svg||width=300]][[image:3 Ebenen C.svg||width=300]][[image:3 Ebenen D.svg||width=300]]
56 +{{/aufgabe}}
3 Ebenen A.svg
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3 Ebenen alle parallel.ggb
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