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(Add whitespace)
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Scriptim committed Dec 11, 2019
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4 changes: 2 additions & 2 deletions Mathe_12_1.tex
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Expand Up @@ -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
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