Vektor – 5 die Lage zwischen zwei Geraden

Man zeige, dass die Gerade h durch die Punkte A und B und
die gerade k durch C und D sich in einem Punkt S schneiden.
Man bestimme den Winkel zwischen h und k.
Ergebnisse
A 1,0 3,0 2,0
1,0 1,0 r= 1,00
g(AB): X = 3,0 + r 5,0 s= 1,00
B 2,0 8,0 5,0 2,0 3,0
C 8,0 13,0 6,0
8,0 -6,0 S
(2
8 5)
g(CD): X = 13,0 + s -5,0
D 2,0 8,0 5,0 6,0 -1,0 α= 136,9 °
Ergebnisse
A 2,0 8,0 5,0 2,0 7,0 r =1,00
g(AB): X = 8,0 + r 10,0 s =0,50
B 9,0 18,0 9,0 5,0 4,0
C 15,0 23,0 10,0 15,0 -12,0 S
(9
18 9)
g(CD): X = 23,0 + s -10,0
D 3,0 13,0 8,0 10,0 -2,0 α= 161,6 °
Ergebnisse
A 1,0 5,0 3,0 1,0 6,0 r =1,00
g(AB): X = 5,0 + r 5,0 s =0,33
B 7,0 10,0 4,0 3,0 1,0
C 8,0 15,0 7,0
8,0 -3,0 S
(7
10 4)
g(CD): X = 15,0 + s -15,0
D 5,0 0,0 -2,0 7,0 -9,0 α= 136,9 °
Ergebnisse
A -1,0 -5,0 -3,0 -1,0 -6,0 r =1,00
g(AB): X = -5,0 + r -5,0 s =0,25
B -7,0 -10,0 -4,0 -3,0 -1,0
C -6,0 -5,0 -1,0
-6,0 -4,0 S
(-7
-10 -4)
g(CD): X = -5,0 + s -20,0
D -10,0 -25,0 -13,0 -1,0 -12,0 α= 43,1 °
Ergebnisse
A -7,0 -12,0 -5,0 -7,0 -11,0 r =1,00
g(AB): X = -12,0 + r -5,0 s =1,00
B -18,0 -17,0 -4,0 -5,0 1,0
C -12,0 -12,0 -3,0
-12,0 -6,0 S
(-18
-17 -4)
g(CD): X = -12,0 + s -5,0
D -18,0 -17,0 -4,0 -3,0 -1,0 α= 19,5 °
Ergebnisse
A -11,0 -7,0 0,0 -11,0 1,0 r =1,00
g(AB): X = -7,0 + r 5,0 s =0,50
B -10,0 -2,0 3,0 0,0 3,0
C -4,0 3,0 4,0
-4,0 -12,0 S
(-10
-2 3)
g(CD): X = 3,0 + s -10,0
D -16,0 -7,0 2,0 4,0 -2,0 α= 136,9 °
Ergebnisse
A -4,0 5,0 5,0
-4,0 12,0 r =1,00
g(AB): X = 5,0 + r 10,0 s =0,25
B 8,0 15,0 7,0 5,0 2,0
C 4,0 20,0 12,0
4,0 16,0 S
(8
15 7)
g(CD): X = 20,0 + s -20,0
D 20,0 0,0 -8,0 12,0 -20,0 α= 95,4 °
Ergebnisse
A
11,0
5,0 -1,0
11,0 -6,0 r =1,00
g(AB): X = 5,0 + r -5,0 s =2,00
B 5,0 0,0 -2,0 -1,0 -1,0
C 1,0 5,0 3,0
1,0 2,0 S
(5
0 -2)
g(CD): X = 5,0 + s -2,5
D 3,0 2,5 0,5 3,0 -2,5 α= 84,6 °