Zusammenfassung Vektoren und Ebenen im Raum - Q2 Gymnasium - Mathematik - Abitur
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Course
Mathematik
Institution
Gymnasium
Das sind Lernzettel für eine Klausur im Gymnasium für die Q2 (G9) im Fach Mathematik. Diese eignen sich auch gut fürs Abitur.
Die Themen die hier erklärt werden sind:
- Punkte und Vektoren im dreiimensionalen Raum zeichnerisch darstellen
- Länge von Vektoren ausrechnen
- Parameterglei...
Punkte und Vektoren im dreidimensionalen Raum Zeichnerisch darstellen
1
Punkt x(2(112)
·
-
2
1 1
- >
Vektor a
3
:
=
7
...
1 !
....................
- -
1
L
Skalarprodukt
a
(ä)
=
5 (55)
=
(a.5 =
a1. b1 +
a z . bz a3.b3
+
-
Wenn Skalarprodukt
0 dann
ist
Orthogonal zueinander 7
, Länge von Vektoren ausrechnen
14
- 3
=
(ü
=
also verschiebtk o m m t
wenn
Ursprung
-> man zum
2
-..
-
--- 3
Pl-2,2,1)
-
man an den Punkt an
---
-2
I h W E >
1 23 i 5
-
I
2
Abstand:Koordinaten von P(-2,2,1) minus (0,0,0)
-3 (
-
also:d =
-
z -
0)(2 0)(1 0)
- -
4
-
5
L d =
- zz 1
->
jetzt
diese Zahlen hoch und addieren und Wurzelziehen
verallgemeinert: a N
T 12
=
+
=An
= ()
=
i
=
=
1
+z =5
d 3
-
=
-
Vektor Vektorlänge
Beispiel:
5 =(
15=E
*62
151 525
36 =
+
151 =
w
151 =
11
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