Wiki-Quellcode von Lösung In Summe Null
Zuletzt geändert von Daniel Stocker am 2024/11/15 20:12
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| author | version | line-number | content |
|---|---|---|---|
| 1 | {{formula}}\begin{align*}\overrightarrow{AB} &= \left(\begin{array}{c} 5-3 \\ 2-1 \\ 4-5\end{array}\right) &= \left(\begin{array}{c} 2 \\ 1 \\ -1\end{array}\right) \\ | ||
| 2 | \overrightarrow{CA} &= \left(\begin{array}{c} 3-8 \\ 1-7 \\ 5-1 \end{array}\right) &= \left(\begin{array}{c} -5 \\ -6 \\ 4 \end{array}\right) \\ | ||
| 3 | \overrightarrow{BC} &= \left(\begin{array}{c} 8-5 \\ 7-2 \\ 1-4 \end{array}\right) &= \left(\begin{array}{c} 3 \\ 5 \\ -3 \end{array}\right) \\ | ||
| 4 | \overrightarrow{DA} &= \left(\begin{array}{c} 3-d_1 \\ 1-d_2 \\ 5-d_3 \end{array}\right) | ||
| 5 | \end{align*} | ||
| 6 | {{/formula}} | ||
| 7 | |||
| 8 | {{formula}} | ||
| 9 | \overrightarrow{AB}-\overrightarrow{CA}+\overrightarrow{BC}-\overrightarrow{DA}&=\overrightarrow{o} | ||
| 10 | {{/formula}} | ||
| 11 | |||
| 12 | {{formula}} | ||
| 13 | \left(\begin{array}{c} 2 \\ 1 \\ -1\end{array}\right)-\left(\begin{array}{c} -5 \\ -6 \\ 4 \end{array}\right) + \left(\begin{array}{c} 3 \\ 5 \\ -3 \end{array}\right) - \left(\begin{array}{c} 3-d_1 \\ 1-d_2 \\ 5-d_3 \end{array}\right) &= \left(\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right) | ||
| 14 | {{/formula}} | ||
| 15 | |||
| 16 | {{formula}} | ||
| 17 | \begin{align*} | ||
| 18 | &\text{I: } &2-(-5)+3-(3-d_1) &= 0 \\ | ||
| 19 | & &10-3+d_1 &= 0\\ | ||
| 20 | & &d_1 &= -7 \\ | ||
| 21 | &\text{II: } &1-(-6)+5-(1-d_2) &= 0 \\ | ||
| 22 | & &12-1+d_2 &= 0\\ | ||
| 23 | & &d_2 &= -11 \\ | ||
| 24 | &\text{III: } &-1-4+(-3)-(5-d_3) &= 0 \\ | ||
| 25 | & &-8-5+d_3 &= 0\\ | ||
| 26 | & &d_3 &= 13 | ||
| 27 | \end{align*} | ||
| 28 | {{/formula}} | ||
| 29 | |||
| 30 | {{formula}} | ||
| 31 | \Rightarrow D(-7|-11|13) | ||
| 32 | {{/formula}} |