Weitere Vektorgeometrie Prüfungsaufgabe

21_22_A/6MT19c_pr1_VECG1/Pruefung.tex

@@ -30,7 +30,8 @@
 \input{P_TALS/vecg1/Vereinfachen_v1}
 
 \section{Linearkombination}
-  
+
+\input{P_TALS/vecg1/LinearkombinationWuerfel_v1}
 \input{P_TALS/vecg1/Linearkombination_v1}
 
 \section{Polarkoordinaten}

21_22_A/6ZVG21n_pr1_AA1/Pruefung.tex

@@ -12,7 +12,7 @@
 %%\renewcommand{\pruefungsTeil}{Teil 1 und 2 mit TR}
 \renewcommand{\pruefungsDatum}{Mo., 20. Sept. 2021}
 %% brauchte 10 Minuten * 4 bei GESO: 40 Min. (Eine Lektion wird etw. knapp.)
-\renewcommand{\pruefungsVorgabeZeit}{45 Minuten}
+\renewcommand{\pruefungsVorgabeZeit}{40 Minuten}
 
 \renewcommand{\inPapierform}{\achtAvier}%% es gibt "achtAvier", "openBook"
 \renewcommand{\pruefungsHilfsmittel}{\defaultHiflsmittelMitRechner{}}

aufgaben/P_TALS/vecg1/AdditionSubtraktion_v1.tex

@@ -1,6 +1,6 @@
 \begin{frage}[2]%% Anzahl Punkte für diese Aufgabe
 
-  Zeichnen Sie zwei Repräsentanten des Vektors $\vec{v}$ mit:
+  Zeichnen Sie einen Repräsentanten des Vektors $\vec{v}$ mit:
   $$\vec{v} = \vec{a} -2\cdot{}\vec{b}$$
   
   \bbwGraphLeer{-4}{4}{-4}{4}{
@@ -12,4 +12,4 @@
 
   \platzFuerBerechnungen{4.4}
   
-  \end{frage} 
+\end{frage} 

aufgaben/P_TALS/vecg1/LinearkombinationWuerfel_v1.tex

@@ -0,0 +1,17 @@
+\begin{frage}[2]%% Anzahl Punkte für diese Aufgabe
+  Betrachten Sie den folgenden Würfel:
+
+  \bbwCenterGraphic{7cm}{P_TALS/vecg1/img/Wuerfel.png}
+
+  Dabei sind $\vec{a}= \overrightarrow{AB}$, $\vec{b} =
+  \overrightarrow{BC}$ und $\vec{c} = \overrightarrow{CG}$ gegeben.
+
+  Der Punkt $M$ teilt die Strecke $\overline{HG}$ im Verhältnis 1:2
+  (siehe Grafik).
+
+  Geben Sie den Vektor $\overrightarrow{BM}$ als Linearkombination der
+  drei Vektoren $\vec{a}$, $\vec{b}$ und $\vec{c}$ an.
+
+  $$\overrightarrow{BM} = \LoesungsRaumLang{-\frac23 \vec{a} + \vec{b} + \vec{c}}$$
+\platzFuerBerechnungen{3.2}%%
+\end{frage} 

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