diff --git a/docs/zusatz.pdf b/docs/zusatz.pdf
index 7607019..19ecb34 100644
Binary files a/docs/zusatz.pdf and b/docs/zusatz.pdf differ
diff --git a/docs/zusatz.tex b/docs/zusatz.tex
index 08ed7e1..37c20e3 100644
--- a/docs/zusatz.tex
+++ b/docs/zusatz.tex
@@ -366,7 +366,7 @@ gelten.
         \begin{mathe}[mc]{cccc}
             v_{1} = \begin{svector} 5\\ 8\\\end{svector},
             &v_{2} = \begin{svector} 25\\ 40\\\end{svector},
-            &v_{3} = \begin{svector} -140\\ 30\\\end{svector},
+            &v_{3} = \begin{svector} 200\\ 320\\\end{svector},
             &v_{4} = \begin{svector} 30\\ 48\\\end{svector}.\\
         \end{mathe}
 
@@ -396,7 +396,7 @@ gelten.
             Wir beachten auch, dass
 
                 \begin{mathe}[mc]{rcccl}
-                    10v_{2}-10v_{1} &= &\begin{svector} -140\\ 30\\\end{svector} &= &v_{3},\\
+                    10v_{2}-10v_{1} &= &\begin{svector} 200\\ 320\\\end{svector} &= &v_{3},\\
                     v_{1}+v_{2} &= &\begin{svector} 30\\ 48\\\end{svector} &= &v_{4}\\
                 \end{mathe}
 
@@ -577,7 +577,7 @@ gelten.
 
         \begin{mathe}[mc]{ccc}
             v_{1} = \begin{svector} 8\\ 0\\ 0\\ 4\\\end{svector},
-            &v_{2} = \begin{svector} 16\\ 0\\ 0\\ 9\\\end{svector},
+            &v_{2} = \begin{svector} 18\\ 0\\ 0\\ 9\\\end{svector},
             &v_{3} = \begin{svector} 2\\ 0\\ 0\\ 1\\\end{svector}.\\
         \end{mathe}
 
@@ -1141,7 +1141,7 @@ gelten.
         \begin{mathe}[mc]{cccc}
             v_{1} = \begin{svector} 0\\ 3\\ 0\\\end{svector},
             &v_{2} = \begin{svector} 1\\ 3\\ 0\\\end{svector},
-            &v_{3} = \begin{svector} 10\\ 0\\ 0\\\end{svector},
+            &v_{3} = \begin{svector} 11\\ 1\\ 1\\\end{svector},
             &v_{4} = \begin{svector} 1\\ 1\\ 1\\\end{svector}.\\
         \end{mathe}