Gegenseitige Lage von zwei Geraden (Fallunterscheidung)
restart;
with(geom3d):
Warning, the assigned name polar now has a global binding
Dazu gibt man als erstes die Gleichung einer Geraden ein
line(g,[-8+2*t,2*t,-3*t],t);
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detail(g);
Warning, assuming that the names of the axes are _x, _y, and _z
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Nun gibt man eine weitere Gleichung einer Geraden ein
line(h,[4*t,8-4*t,-6*t],t);
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
detail(h);
Warning, assuming that the names of the axes are _x, _y, and _z
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Man kann die Geradengleichungen jetzt in ein Koordinatensystem zeichnen, um die gegenseitige Lage der beiden Geraden zu pr\303\274fen
draw([g,h],axes=normal);
NigtJSdDVVJWRVNHNiM3JDclJCErXTcyJkciISIpJCErK0RyXVshIiokIitdKG9nRihGLTclJCErK3ZHXEpGLSQiKytEcl1bRi0kIStdKG9nRihGLS1GJDYjNyQ3JUYoJCIrXTcyJjMjRiokIit2b2dGPkYqNyUkIitdNzImRyJGKiQhKl03MiZbRiokISt2b2dGPkYqLSUqQVhFU1NUWUxFRzYjJSdOT1JNQUxHLSUsT1JJRU5UQVRJT05HNiQkISRJJyEiIiQhJF0mRk8tJSVWSUVXRzYlOyQhKkRyXUciISIoJCIqRHJdRyJGWDskISlEcl1bRlgkIipEcl0zI0ZYO0ZEJCIyKysrXShvZ0Y+ISM6LSUoU0NBTElOR0c2IyUsQ09OU1RSQUlORURH
Man erkennt, dass die beiden Geraden zueinander windschief sind, es gibt also keinen Schnittpunkt, das kann man auch folgenderma\303\237en \303\274berpr\303\274fen
intersection(S,g,h);
intersection:, "the given objects do not intersect"
Wir geben nun eine neue Gleichung einer Geraden ein
line(k,[-8+2*t,8+2*t,3*t],t);
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detail(k);
Warning, assuming that the names of the axes are _x, _y, and _z
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draw([h,k],axes=normal);
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Man erkennt nun, dass sich die Geraden h und k in genau einem Punkt schneiden , wir bestimmen nun den genauen Schnittpunkt
intersection(P,h,k);
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detail(P);
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Der Schnittpunkt hei\303\237t also: P(-4|12|6)
Wir geben nun zwei neue Geradengleichungen ein
line(m,[-8+4*t,8+4*t,6*t],t);
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
detail(m);
Warning, assuming that the names of the axes are _x, _y, and _z
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draw([k,m],axes=normal);
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Man erkennt, dass die beiden Geraden identisch sind, \303\274berpr\303\274fen wir das noch einmal:
intersection(B,k,m);
areinterl:, "the two lines k and m are the same"
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