Änderungen von Dokument BPE 16.5 Gegenseitige Lage von Ebenen und Geraden
Zuletzt geändert von Anna Kukin am 2026/05/25 18:19
Von Version 28.1
bearbeitet von Holger Engels
am 2026/04/28 13:11
am 2026/04/28 13:11
Änderungskommentar:
Anhang 3 Ebenen davon zwei parallel.svg verschoben nach 3 Ebenen C.svg.
Auf Version 39.1
bearbeitet von Anna Kukin
am 2026/05/02 21:22
am 2026/05/02 21:22
Änderungskommentar:
Es gibt keinen Kommentar für diese Version
Zusammenfassung
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Seiteneigenschaften (3 geändert, 0 hinzugefügt, 0 gelöscht)
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Anhänge (0 geändert, 1 hinzugefügt, 1 gelöscht)
Details
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- Titel
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... ... @@ -1,1 +1,1 @@ 1 -BPE 16.5 Gegenseitige Lage von Ebenen 1 +BPE 16.5 Gegenseitige Lage von Ebenen und Geraden - Dokument-Autor
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... ... @@ -1,1 +1,1 @@ 1 -XWiki. holgerengels1 +XWiki.akukin - Inhalt
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... ... @@ -22,35 +22,36 @@ 22 22 {{aufgabe id="Lösungsmenge geometrisch" afb="II" kompetenzen="K6" quelle="Frauke Beckstette" zeit="12"}} 23 23 Ordne den folgenden linearen Gleichungssystemen jeweils die passende Abbildung zu. Begründe deine Entscheidung. 24 24 Visualisiere das verbliebene LGS analog. 25 - (%class="abc horiz"%)26 - 1.(%style="vertical-align:top"%){{formula}}27 -\begin{aligned} 25 + 26 +(% class="abc horiz" %) 27 +1. (% style="vertical-align: top" %){{formula}}\begin{aligned} 28 28 x_1 + x_2 &= 1 \\ 29 29 - 3x_2 &= 8 \\ 30 30 -x_1 + 2x_2 + x_3 &= 4 31 -\end{aligned} 32 -{{/formula}} 33 -1. (%style="vertical-align: top"%){{formula}} 34 -\begin{aligned} 31 +\end{aligned}{{/formula}} 32 +1. (% style="vertical-align: top" %){{formula}}\begin{aligned} 35 35 3x_1 - 2x_2 + x_3 &= 7 \\ 36 36 -6x_1 + 4x_2 - 2x_3 &= 3 \\ 37 37 15x_1 - 10x_2 + 5x_3 &= 5 38 -\end{aligned} 39 -{{/formula}} 40 -1. (%style="vertical-align: top"%){{formula}} 41 -\begin{aligned} 36 +\end{aligned}{{/formula}} 37 +1. (% style="vertical-align: top" %){{formula}}\begin{aligned} 42 42 2x_1 - 2x_2 + 2x_3 &= 2 \\ 43 43 -2x_1 - 6x_2 + 2x_3 &= 0 \\ 44 44 2x_1 + 2x_2 &= 1 45 -\end{aligned} 46 -{{/formula}} 47 -1. (%style="vertical-align: top"%){{formula}} 48 -\begin{aligned} 41 +\end{aligned}{{/formula}} 42 +1. (% style="vertical-align: top" %){{formula}}\begin{aligned} 49 49 x_1 + 3x_2 - 2x_3 &= 5 \\ 50 50 -2x_1 - 6x_2 + 4x_3 &= 1 \\ 51 51 2x_1 + x_3 &= 3 52 -\end{aligned} 53 -{{/formula}} 46 +\end{aligned}{{/formula}} 54 54 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]]48 +[[image:3 Ebenen A.svg||width="200"]][[image:3 Ebenen B.svg||width="200"]][[image:3 Ebenen C.svg||width="200"]] 56 56 {{/aufgabe}} 50 + 51 +{{aufgabe id="" afb="I, II" kompetenzen="K2, K4, K5" quelle="[[IQB e.V.>>https://www.iqb.hu-berlin.de/media/exercise_files/Abituraufgaben_Mathematik/2017MerhoehtAAGLAA211_Aufgabe.pdf]]" zeit="15" niveau="e" tags="iqb" cc="BY"}} 52 +Gegeben sind die Ebene {{formula}}E: x_1 + x_2 + 2x_3 = 4{{/formula}} und \\ 53 +die Gerade {{formula}}g: \vec{x} = \begin{pmatrix} 2 \\ 1 \\ -2 \end{pmatrix} + \lambda \cdot \begin{pmatrix} 2 \\ -1 \\ -3 \end{pmatrix}{{/formula}} mit {{formula}}\lambda \in \mathbb{R}{{/formula}}. 54 +(%class=abc%) 55 +1. Zeichne die Schnittgerade von {{formula}}E{{/formula}} mit der {{formula}}x_2x_3{{/formula}}-Ebene in ein Koordinatensystem ein. 56 +1. Berechne die Koordinaten des Schnittpunktes von {{formula}}E{{/formula}} und {{formula}}g{{/formula}}. 57 +{{/aufgabe}}
- 3 Ebenen schneiden sich in einer Gerade.svg
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- Author
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... ... @@ -1,1 +1,0 @@ 1 -XWiki.holgerengels - Größe
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... ... @@ -1,1 +1,0 @@ 1 -4.6 KB - Inhalt
- 3 Ebenen X.svg
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- Author
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
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... ... @@ -1,0 +1,1 @@ 1 +4.2 KB - Inhalt
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