Geraden 2012 13: Unterschied zwischen den Versionen
Aus Geometrie-Wiki
(→Definition des Normalenvektors) |
(→Definition des Normalenvektors) |
||
Zeile 12: | Zeile 12: | ||
<br> | <br> | ||
<ggb_applet width="600" height="400" version="4.2" ggbBase64="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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /> | <ggb_applet width="600" height="400" version="4.2" ggbBase64="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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /> | ||
+ | |||
+ | === Eigenschaften des Normalenvektors === | ||
+ | |||
+ | Sei g eine Gerade mit <math> \ \ g = \vec{s} + \lambda \cdot \vec{t} \ und vec{n} der Normalen</math> | ||
+ | |||
+ | E1: Der Normalenvektor und |
Version vom 9. Januar 2013, 16:27 Uhr
Der Normalenvektor
Definition des Normalenvektors
Sei g eine Gerade und A ein Punkt auf dieser Geraden. Ein Vektor heisst Normalenvektor von g am Aufpunkt A genau dann, wenn folgendes gilt:
i) steht senkrecht auf der Gerade g
ii)
Skizze eines Normalenvektors
Eigenschaften des Normalenvektors
Sei g eine Gerade mit
E1: Der Normalenvektor und