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Zusammenfassung Geometrie Mathematik Abitur
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Diese Zusammenfassung enthält alle wichtigen Bereiche zum Teil Geometrie, welcher ein wichtiger Teil des Mathematikabiturs ist.
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Geometrie Mathematik Abitur 2023Skalarprodukt: a°b= a1b1 + a2b2 + a3b3
—> Länge eines Vektors /a/ = Wurzel a°a = Wurzel a1^2 + a2^2 + a3^2
—> Senkrechte Lage zweier Vektoren
—> Winkel zwischen zwei Vektoren: cos q
Kreuzprodukt: axb= ...
—> ein zu zwei Vektoren senkrechter Vektor c= axb
—> Flächeninhalt eines Parallelograms /axb/
—> Volumen eines Spats/ dreiseitige Pyramide /a°(bxc)/ bzw. 1/6 * /a°(bxc)
Geraden: g: x= A + u * AB
—> Parallel zur x1x2-Ebene, wenn x3=0 (1/1/0)
—> Parallel zur x1x3-Ebene, wenn x2=0 (1/0/1)
—> Parallel zur x2x3-Ebene, wenn x1=0 (0/1/1)
—> Parallel zur x1-Achse: (1/0/0); x2-Achse: (0/1/0); x3-Achse: (0/0/1)
Ebenen: E: x= A + u * AB + v * AC (Parameterform)
E: n1x1 + n2x2 + n3x3 + n0 = 0 (Normalenform)
—> Parallel zur x1x2-Ebene, wenn n= a*(0/0/1)
—> Parallel zur x1x3-Ebene, wenn n= a*(0/1/0)
—> Parallel zur x2x3-Ebene, wenn n= a*(1/0/0)
—> Parallel zur x1-Achse: x1 von n=0, zur x2-Achse: x2 von n=0, zur x3-Achse: x3 von n=0
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