Lagebeziehungen
Welche Lagebeziehungen gibt es?
In der Ebene können Geraden als Graphen linearer Funktionen [b]parallel verlaufen[/b], [b]zusammen fallen[/b] oder [b]sich in einem Punkt schneiden[/b]. [br][br]Die Lage zweier Geraden zueinander kann [color=#38761D]geometrisch[/color] anhand [color=#38761D]der Graphen[/color][br]im Koordinatensystem oder [color=#1155Cc]algebraisch[/color] mithilfe der [color=#1155Cc]Funktionsgleichungen[/color] beschrieben werden.[br][br][img]https://www.geogebra.org/resource/Xsfj7Unz/b8pGoWIhlaRqh2cc/material-Xsfj7Unz.png[/img]
Darstellungsarten für Geraden
Es gibt verschiedene Arten wie eine Gerade in der Ebene dargestellt werden kann:[br][br][list][*][b]Hauptform[/b]: Diese Form kennst du bereits, man schreibt [math]f:y=mx+b[/math]. m beschreibt die Steigung, b beschreibt den y-Achsenabschnitt.[/*][*][b]Parameterform[/b] (auch Punkt-Richtungsform): In dieser Form wird eine Gerade mit einem Punkt auf der Gerade (als Ortsvektor) und einer Richtung (als Richtungsvektor beschrieben. Man schreibt [math]y=\vec{a}+r\vec{b},r\in\mathbb{R};a,b\in\mathbb{R}^2[/math][/*][/list][br]Dies sind die wichtigsten beiden Darstellungsarten, daneben gibt es aber auch noch folgende Formen, die Normalenform und die allgemeine Form; Diese schauen wir uns später (als Hinführung zur Lagebeziehung von Ebenen an)
Wann sind zwei Geraden parallel?
Gegeben sind hier wieder zwei Geraden , diesesmal aber in [b]Parameterdarstellung[/b].[br][br]Die rote Gerade hat die Form: [math]f:\binom{y_1}{y_2}=\binom{a}{b}+\lambda\binom{c}{d};a,b,c,d\in\Re[/math]. Die Variablen a,b,c und d kannst du mit Schiebereglern verschieben.[br][br][list][*]Beschreibe wie a,b,c und d mit den Vektoren u und v zusammenhängen.[/*][*]Finde mehrere Möglichkeiten wie du die Gerade f parallel zur Geraden legen kannst. Welche Form muss der Vektor [math]\binom{c}{d}[/math] haben, damit die Geraden parallel sind?[br][/*][/list]
Lagebeziehungen von Geraden in 3D
Gegeben sind die Geraden:[br][img]data:image/png;base64,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[/img] (rot)[br]und[br][img]data:image/png;base64,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[/img](blau)[br]Versuche mehrere Möglichkeiten zu finden, den Vektor [img]data:image/png;base64,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[/img]zu wählen, so dass die Geraden identisch sind.