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Schwerpunkt Dreieck Berechnen Beispiel Essay

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Big Work hard essay dream

Unter Verwendung von als Mittelpunkt der Strecke lassen sich die Koordinaten des Schwerpunktes folgendermaßen angeben:

hat die Koordinaten und

In die Koordinaten von S eingesetzt liefert das die folgenden Werte für den Schwerpunkt :

Für den dreidimensionalen Fall lassen sich die Überlegungen analog führen, und für den Schwerpunkt gilt:

  • Beipiel 1: Es sind die Koordinaten des Schwerpunktes S des Dreiecks mit den Punkten zu ermitteln.

Nach oben angegebener Formel ist:

Schwerpunkt in Vektordarstellung

Es seien die Ortsvektoren der Eckpunkte des Dreiecks , der Ortsvektor von (Halbierungspunkt von ) und der Ortvektor des Schwerpunktes S.

Dann gilt , und wegen erhält man:

  • Beispiel 2: Man ermittle den Ortsvektor des Schwerpunktes S vom Dreieck mit den Punkten .

Es ist:

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