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 13.4
bearbeitet von Dirk Tebbe
am 2026/04/28 09:59
am 2026/04/28 09:59
Änderungskommentar:
Es gibt keinen Kommentar für diese Version
Auf Version 31.1
bearbeitet von Holger Engels
am 2026/04/28 13:16
am 2026/04/28 13:16
Änderungskommentar:
Anhang 3 Ebenen B.svg verschoben nach 3 Ebenen X.svg.
Zusammenfassung
-
Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
-
Anhänge (0 geändert, 8 hinzugefügt, 0 gelöscht)
Details
- Seiteneigenschaften
-
- Dokument-Autor
-
... ... @@ -1,1 +1,1 @@ 1 -XWiki. dirktebbe1 +XWiki.holgerengels - Inhalt
-
... ... @@ -12,7 +12,7 @@ 12 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. 13 13 {{/aufgabe}} 14 14 15 -{{aufgabe id="Schnittgerade" afb="II" kompetenzen="K1, K 4" quelle="Martin Stern, Dirk Tebbe" zeit="15"}}15 +{{aufgabe id="Schnittgerade" afb="II" kompetenzen="K1, K6" quelle="Martin Stern, Dirk Tebbe" zeit="15"}} 16 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}}. 17 17 (%class=abc%) 18 18 1. Bestimme die Schnittgerade //g//. ... ... @@ -19,4 +19,38 @@ 19 19 1. Welche besondere Lage haben die beiden Ebenen zueinander? 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}} 22 22 55 +[[image:3 Ebenen A.svg||width=200]][[image:3 Ebenen B.svg||width=200]][[image:3 Ebenen C.svg||width=200]][[image:3 Ebenen D.svg||width=200]] 56 +{{/aufgabe}}
- 3 Ebenen A.svg
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +4.6 KB - Inhalt
-
... ... @@ -1,0 +1,1 @@ 1 +<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="633" height="617"><defs><clipPath id="fJMIKBCQmWqk"><path fill="none" stroke="none" d=" M 0 0 L 633 0 L 633 617 L 0 617 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#fJMIKBCQmWqk)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="634" height="618" fill-opacity="1"/><path fill="rgb(21,101,192)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 166.50000000000006 155.50000000000006 L 566.4999999999999 355.5 L 466.49999999999994 455.49999999999994 L 66.50000000000011 255.5 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(0,103,88)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 566.4999999999999 155.50000000000006 L 166.50000000000006 355.5 L 66.50000000000011 455.49999999999994 L 466.49999999999994 255.5 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(241,194,50)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 216.50000000000006 155.50000000000006 L 316.5 555.5 L 416.49999999999994 455.49999999999994 L 316.5 55.50000000000006 Z" fill-opacity="0.09803921568627451"/><path fill="none" stroke="rgb(211,47,47)" paint-order="fill stroke markers" d=" M 265.5 355.5 L 365.5 255.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="3.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 166.50000000000006 155.50000000000006 L 566.4999999999999 355.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 566.4999999999999 355.5 L 466.49999999999994 455.49999999999994" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 466.49999999999994 455.49999999999994 L 66.50000000000011 255.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 66.50000000000011 255.5 L 166.50000000000006 155.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 566.4999999999999 155.50000000000006 L 166.50000000000006 355.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 166.50000000000006 355.5 L 66.50000000000011 455.49999999999994" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 66.50000000000011 455.49999999999994 L 466.49999999999994 255.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 466.49999999999994 255.5 L 566.4999999999999 155.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 216.50000000000006 155.50000000000006 L 316.5 555.5" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 316.5 555.5 L 416.49999999999994 455.49999999999994" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 416.49999999999994 455.49999999999994 L 316.5 55.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 316.5 55.50000000000006 L 216.50000000000006 155.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/></g></g></svg>
- 3 Ebenen C.svg
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +5.0 KB - Inhalt
-
... ... @@ -1,0 +1,1 @@ 1 +<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="633" height="617"><defs><clipPath id="cwJQsrfdJKJV"><path fill="none" stroke="none" d=" M 0 0 L 633 0 L 633 617 L 0 617 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#cwJQsrfdJKJV)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="634" height="618" fill-opacity="1"/><path fill="rgb(21,101,192)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 188.50000000000009 382.50000000000006 L 596.5 279.50000000000034 L 488.5 382.50000000000006 L 88.50000000000011 482.4999999999998 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(0,103,88)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 538.5 132.50000000000068 L 138.5000000000001 232.50000000000045 L 38.500000000000114 332.50000000000017 L 438.5 232.50000000000045 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(241,194,50)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 188.50000000000009 132.50000000000068 L 338.50000000000006 582.4999999999995 L 438.5 482.4999999999998 L 288.50000000000006 32.500000000000966 Z" fill-opacity="0.09803921568627451"/><path fill="none" stroke="rgb(211,47,47)" paint-order="fill stroke markers" d=" M 288.50000000000006 432.49999999999994 L 388.5 332.50000000000017" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="3.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 188.50000000000009 382.50000000000006 L 596.5 279.50000000000034" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 596.5 279.50000000000034 L 488.5 382.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 488.5 382.50000000000006 L 88.50000000000011 482.4999999999998" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 88.50000000000011 482.4999999999998 L 188.50000000000009 382.50000000000006" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 538.5 132.50000000000068 L 138.5000000000001 232.50000000000045" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 138.5000000000001 232.50000000000045 L 38.500000000000114 332.50000000000017" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 38.500000000000114 332.50000000000017 L 438.5 232.50000000000045" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 438.5 232.50000000000045 L 538.5 132.50000000000068" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 188.50000000000009 132.50000000000068 L 338.50000000000006 582.4999999999995" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 338.50000000000006 582.4999999999995 L 438.5 482.4999999999998" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 438.5 482.4999999999998 L 288.50000000000006 32.500000000000966" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 288.50000000000006 32.500000000000966 L 188.50000000000009 132.50000000000068" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(211,47,47)" paint-order="fill stroke markers" d=" M 238.50000000000006 282.50000000000034 L 338.50000000000006 182.50000000000057" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="3.5"/></g></g></svg>
- 3 Ebenen D.svg
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +4.6 KB - Inhalt
- 3 Ebenen X.svg
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +4.2 KB - Inhalt
-
... ... @@ -1,0 +1,1 @@ 1 +<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="633" height="617"><defs><clipPath id="sRGXtZPVAmBF"><path fill="none" stroke="none" d=" M 0 0 L 633 0 L 633 617 L 0 617 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#sRGXtZPVAmBF)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="634" height="618" fill-opacity="1"/><path fill="rgb(21,101,192)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 166.5 302.49999999999966 L 574.5 199.49999999999983 L 466.5 302.49999999999966 L 66.5 402.49999999999943 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(0,103,88)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 566.5 102.50000000000001 L 166.5 202.49999999999983 L 66.5 302.49999999999966 L 466.5 202.49999999999983 Z" fill-opacity="0.09803921568627451"/><path fill="rgb(241,194,50)" stroke="none" paint-order="stroke fill markers" fill-rule="evenodd" d=" M 66.5 502.4999999999992 L 466.5 402.49999999999943 L 566.5 302.49999999999966 L 166.5 402.49999999999943 Z" fill-opacity="0.09803921568627451"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 166.5 302.49999999999966 L 574.5 199.49999999999983" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 574.5 199.49999999999983 L 466.5 302.49999999999966" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 466.5 302.49999999999966 L 66.5 402.49999999999943" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(21,101,192)" paint-order="fill stroke markers" d=" M 66.5 402.49999999999943 L 166.5 302.49999999999966" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 566.5 102.50000000000001 L 166.5 202.49999999999983" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 166.5 202.49999999999983 L 66.5 302.49999999999966" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 66.5 302.49999999999966 L 466.5 202.49999999999983" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(0,103,88)" paint-order="fill stroke markers" d=" M 466.5 202.49999999999983 L 566.5 102.50000000000001" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 66.5 502.4999999999992 L 466.5 402.49999999999943" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 466.5 402.49999999999943 L 566.5 302.49999999999966" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 566.5 302.49999999999966 L 166.5 402.49999999999943" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/><path fill="none" stroke="rgb(241,194,50)" paint-order="fill stroke markers" d=" M 166.5 402.49999999999943 L 66.5 502.4999999999992" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/></g></g></svg>
- 3 Ebenen alle parallel.ggb
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +28.0 KB - Inhalt
- 3 Ebenen davon zwei parallel.ggb
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +30.6 KB - Inhalt
- 3 Ebenen schneiden sich in einem Punkt.ggb
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +28.3 KB - Inhalt
- 3 Ebenen schneiden sich in einer Gerade.ggb
-
- Author
-
... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
-
... ... @@ -1,0 +1,1 @@ 1 +26.5 KB - Inhalt