diff --git a/Mathe.pdf b/Mathe.pdf
index 4b93797..c1ab285 100644
Binary files a/Mathe.pdf and b/Mathe.pdf differ
diff --git a/Mathe_12_1.tex b/Mathe_12_1.tex
index 8d2548a..c9afa7f 100644
--- a/Mathe_12_1.tex
+++ b/Mathe_12_1.tex
@@ -2038,8 +2038,8 @@ \section{Kreuzprodukt}
   \vv{a} \cdot \vv{x} = 0 \qquad \text{\Rmnum{1}} \quad a_1x_1 + a_2x_2 + a_3x_3 = 0 \\
   \vv{b} \cdot \vv{x} = 0 \qquad \text{\Rmnum{2}} \quad b_1x_1 + b_2x_2 + b_3x_3 = 0 \\\\
   b_1 \cdot \text{\Rmnum{1}} - a_1 \cdot \text{\Rmnum{2}} \\
-  \text{\Rmnum{1}} a_1x_1 + a_2x_2 + a_3x_3 = 0 \\
-  \text{\Rmnum{2}} 0 + (b_1a_2 - a_1b_2)x_2 + (b_1a_3-a_1b_3)x_3 = 0 \\\\
+  \text{\Rmnum{1}} \quad a_1x_1 + a_2x_2 + a_3x_3 = 0 \\
+  \text{\Rmnum{2}} \quad 0 + (b_1a_2 - a_1b_2)x_2 + (b_1a_3-a_1b_3)x_3 = 0 \\\\
   \text{willkürlich } x_2 = a_3b_1 - a_1b_3 \\
   \Rightarrow x_3 = -(a_2b_1 - a_1b_2) = a_1b_2 - a_2b_1 \\
   \Rightarrow x_1 = a_2b_3 - a_3b_2