Flächeninhalt eines Trapezes

Die Aufgabenstellung
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[/img][br]Der Vektor [math]\vec{h}[/math] soll vom Punkt [math]P_2[/math] auf einen Punkt auf der Geraden [math]b[/math] zeigen.[br]Dann muss der Ortsvektor [math]\vec{p}_2[/math] und der Vetkor [math]\vec{h}[/math] zusammen ein Ortsbektor [math]\vec{b}[/math] der Geraden b ergeben.
[math]P1 \, := \, \left(\frac{-3}{2} \; \sqrt{2} - 2, \frac{3}{2} \; \sqrt{2} - 2, 2 \; \sqrt{2} \right) \\ P2 \, := \, \left(\frac{\sqrt{2} + 3}{2}, \frac{-\sqrt{2} + 3}{2}, -3 \cdot \frac{\sqrt{2}}{2} \right) \\ P3 \, := \, \left(4 \; \sqrt{2} + \frac{3}{2}, \frac{3}{2} - 4 \; \sqrt{2}, \frac{-3}{2} \; \sqrt{2} \right) \\ P4 \, := \, \left(\frac{7}{2} \; \sqrt{2} - 2, \frac{-7}{2} \; \sqrt{2} - 2, 2 \; \sqrt{2} \right) \\ \text{a)} \\ \text{Mit dem Befehl Vieleck kann man jetzt das Trapez zeichnen.} \\ \text{Man erhält sogar schon den gesuchen Flächeninhalt.} \\ v1:=59.5 \\ \text{b)} \\ p1 \, := \, \left( \begin{align}\frac{-3}{2} \; \sqrt{2} - 2 \\ \frac{3}{2} \; \sqrt{2} - 2 \\ 2 \; \sqrt{2} \end{align} \right) \\ p2 \, := \, \left( \begin{align}\frac{\sqrt{2} + 3}{2} \\ \frac{-\sqrt{2} + 3}{2} \\ -3 \cdot \frac{\sqrt{2}}{2} \end{align} \right) \\ p3 \, := \, \left( \begin{align}4 \; \sqrt{2} + \frac{3}{2} \\ \frac{3}{2} - 4 \; \sqrt{2} \\ \frac{-3}{2} \; \sqrt{2} \end{align} \right) \\ p4 \, := \, \left( \begin{align}\frac{7}{2} \; \sqrt{2} - 2 \\ \frac{-7}{2} \; \sqrt{2} - 2 \\ 2 \; \sqrt{2} \end{align} \right) \\ o_a \, := \, \left( \begin{align}\frac{1}{2} \; \left(\sqrt{2} + 3 \right) \\ \frac{1}{2} \; \left(-\sqrt{2} + 3 \right) \\ \frac{-3}{2} \; \sqrt{2} \end{align} \right) \\ r_a \, := \, \left( \begin{align}\frac{7}{2} \; \sqrt{2} \\ \frac{-7}{2} \; \sqrt{2} \\ 0 \end{align} \right) \\ a \, := \, \left( \begin{align}\frac{7}{2} \; \sqrt{2} \; λ + \frac{1}{2} \; \left(\sqrt{2} + 3 \right) \\ \frac{-7}{2} \; \sqrt{2} \; λ + \frac{1}{2} \; \left(-\sqrt{2} + 3 \right) \\ \frac{-3}{2} \; \sqrt{2} \end{align} \right) \\ \text{c)} \\ o_b \, := \, \left( \begin{align}\frac{-3}{2} \; \sqrt{2} - 2 \\ \frac{3}{2} \; \sqrt{2} - 2 \\ 2 \; \sqrt{2} \end{align} \right) \\ r_b \, := \, \left( \begin{align}5 \; \sqrt{2} \\ -5 \; \sqrt{2} \\ 0 \end{align} \right) \\ b \, := \, \left( \begin{align}5 \; \sqrt{2} \; μ - \frac{3}{2} \; \sqrt{2} - 2 \\ -5 \; \sqrt{2} \; μ + \frac{3}{2} \; \sqrt{2} - 2 \\ 2 \; \sqrt{2} \end{align} \right) \\ \left( \begin{align}-5 \; \sqrt{2} \; x + \frac{7}{2} \; \sqrt{2} \\ 5 \; \sqrt{2} \; x - \frac{7}{2} \; \sqrt{2} \\ 0 \end{align} \right) \\ \left\{ x = \frac{7}{10} \right\} \\ \left\{ x = \frac{7}{10} \right\} \\ \text{Alle drei Gleichungen werden durch x=7/10 erfüllt.} \\ \text{Damit ist der Richtungsvektor von a ein Vielfaches des Richtungsvektors} \\ \text{von b und die beiden Geraden sind parallel.} \\ \text{d)} \\ \text{Den Vektor h definiere ich zunächst ganz allgemein:} \\ h \, := \, \left( \begin{align}hx \\ hy \\ hz \end{align} \right) \\ \text{Der Vektor h muss zur Geraden a und damit zum Richtungsvektor} \\ \text{r_a senkrecht sein. Das Skalarprodukt muss 0 sein.} \\ Gleichung_1: \, \frac{7}{2} \; \sqrt{2} \; hx - \frac{7}{2} \; \sqrt{2} \; hy = 0 \\ \text{Der Vektor soll in P2 beginnnen und auf einem Punkt von b enden} \\ \text{Das bedeutet, dass der Vektor p2+h auf der Geraden b liegt. (siehe Zeichnung)} \\ \left( \begin{align}hx + \frac{1}{2} \; \left(\sqrt{2} + 3 \right) \\ hy + \frac{1}{2} \; \left(-\sqrt{2} + 3 \right) \\ hz - \frac{3}{2} \; \sqrt{2} \end{align} \right) = \left( \begin{align}5 \; \sqrt{2} \; μ - \frac{3}{2} \; \sqrt{2} - 2 \\ -5 \; \sqrt{2} \; μ + \frac{3}{2} \; \sqrt{2} - 2 \\ 2 \; \sqrt{2} \end{align} \right) \\ \text{Besser in Geogebra:} \\ \left( \begin{align}-5 \; \sqrt{2} \; μ + hx + \frac{1}{2} \; \left(4 \; \sqrt{2} + 7 \right) \\ 5 \; \sqrt{2} \; μ + hy + \frac{1}{2} \; \left(-4 \; \sqrt{2} + 7 \right) \\ hz - \frac{7}{2} \; \sqrt{2} \end{align} \right) \\ Gleichung_2: \, -5 \; \sqrt{2} \; μ + hx + \frac{1}{2} \; \left(4 \; \sqrt{2} + 7 \right) = 0 \\ Gleichung_3: \, 5 \; \sqrt{2} \; μ + hy + \frac{1}{2} \; \left(-4 \; \sqrt{2} + 7 \right) = 0 \\ Gleichung_4: \, hz - \frac{7}{2} \; \sqrt{2} = 0 \\ \text{Die 4 Gleichungen kann man nun lösen:} \\ \left\{ \left\{ hx = \frac{-7}{2}, hy = \frac{-7}{2}, hz = 7 \cdot \frac{\sqrt{2}}{2}, μ = \frac{2}{5} \right\} \right\} \\ \text{Der gesuchte Vektor erhält man nun durch Einsetzen:} \\ hh \, := \, \left( \begin{align}\frac{-7}{2} \\ \frac{-7}{2} \\ \frac{7}{2} \; \sqrt{2} \end{align} \right) \\ \text{e)} \\ \text{Die Grundseite ist der Abstand P2,P3 und die Oberseite ist der Abstand} \\ \text{der Punkte P1,P4} \\ \text{Die Höhe ist der Betrag von h} \\ 7 \\ 7 \\ 10 \\ \frac{119}{2} \\ 59.5[/math][br]

Information: Flächeninhalt eines Trapezes