Änderungen von Dokument Lösung In Summe Null

Zusammenfassung

• Seiteneigenschaften (3 geändert, 0 hinzugefügt, 0 gelöscht)

Details

Seiteneigenschaften

Titel

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1		-Lösung In Summe Null
	1	+Lösung Vektoraddition

Dokument-Autor

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1		-XWiki.akukin
	1	+XWiki.daniel2217

Inhalt

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1		-{{formula}}
2		-\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) \\
3		-\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) \\
4		-\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) \\
	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) \\
5	5	\overrightarrow{DA} &= \left(\begin{array}{c} 3-d_1 \\ 1-d_2 \\ 5-d_3 \end{array}\right)
6	6	\end{align*}
7	7	{{/formula}}
8	8
9		-{{formula}}\overrightarrow{AB}-\overrightarrow{CA}+\overrightarrow{BC}-\overrightarrow{DA}=\overrightarrow{o}{{/formula}}
10		-
11		-{{formula}}\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){{/formula}}
12		-
13	13	{{formula}}
14		-\begin{align*}
15		-&\text{I: } &2-(-5)+3-(3-d_1) &= 0 \\
16		-& &10-3+d_1 &= 0\\
17		-& &d_1 &= -7 \\
18		-&\text{II: } &1-(-6)+5-(1-d_2) &= 0 \\
19		-& &12-1+d_2 &= 0\\
20		-& &d_2 &= -11 \\
21		-&\text{III: } &-1-4+(-3)-(5-d_3) &= 0 \\
22		-& &-8-5+d_3 &= 0\\
23		-& &d_3 &= 13
24		-\end{align*}
	9	+\overrightarrow{AB}-\overrightarrow{CA}+\overrightarrow{BC}-\overrightarrow{DA}&=\overrightarrow{o}
25	25	{{/formula}}
26	26
27	27	{{formula}}
28		-\Rightarrow D(-7|-11|13)
	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)
29	29	{{/formula}}
30	30
31		-
32		-
	16	+{{formula}}
	17	+\text{I:}
	18	+{{/formula}}