Wiki-Quellcode von Entwurf
Version 9.6 von Torben Würth am 2024/02/06 16:41
Zeige letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
| 1 | == Vektoren == | ||
| 2 | |||
| 3 | {{aufgabe id="Vektoraddition zeichnerisch" afb="I" kompetenzen="K5" quelle="Torben Würth" cc="BY-SA" zeit="6"}} | ||
| 4 | Zeichne ein zweidimensionales Koordinatensystem und ermittle zeichnerisch {{formula}}\vec{a}+\vec{b}{{/formula}} | ||
| 5 | a) | ||
| 6 | {{formula}}\vec{a}= \left(\begin{array}{c}1\\3 \end{array}\right){{/formula}} ; {{formula}}\vec{b}= \left(\begin{array}{c}2\\4 \end{array}\right){{/formula}} | ||
| 7 | b) | ||
| 8 | {{formula}}\vec{a}= \left(\begin{array}{c}-1\\2 \end{array}\right){{/formula}} ; {{formula}}\vec{b}= \left(\begin{array}{c}3\\-4 \end{array}\right){{/formula}} | ||
| 9 | {{/aufgabe}} | ||
| 10 | |||
| 11 | {{aufgabe id="Vektoraddition zeichnerisch 2" afb="I" kompetenzen="K5" quelle="Torben Würth" cc="BY-SA" zeit="8"}} | ||
| 12 | Zeichne ein zweidimensionales Koordinatensystem und ermittle zeichnerisch {{formula}}\vec{a}+\vec{b}+\vec{c}{{/formula}} | ||
| 13 | a) | ||
| 14 | {{formula}}\vec{a}= \left(\begin{array}{c}2\\3 \end{array}\right){{/formula}} ; {{formula}}\vec{b}= \left(\begin{array}{c}4\\1 \end{array}\right){{/formula}} ; {{formula}}\vec{c}= \left(\begin{array}{c}-1\\2 \end{array}\right){{/formula}} | ||
| 15 | b) | ||
| 16 | {{formula}}\vec{a}= \left(\begin{array}{c}-2\\2 \end{array}\right){{/formula}} ; {{formula}}\vec{b}= \left(\begin{array}{c}3\\-4 \end{array}\right){{/formula}} {{formula}}\vec{c}= \left(\begin{array}{c}3\\3\end{array}\right){{/formula}} | ||
| 17 | {{/aufgabe}} | ||
| 18 | |||
| 19 | {{aufgabe id="Vektoraddition rechnerisch" afb="I" kompetenzen="K5" quelle="Torben Würth" cc="BY-SA" zeit="6"}} | ||
| 20 | Berechne | ||
| 21 | a) | ||
| 22 | {{formula}}\left(\begin{array}{c}12\\7 \end{array}\right)+\left(\begin{array}{c}2\\4 \end{array}\right)={{/formula}} | ||
| 23 | b) | ||
| 24 | {{formula}}\left(\begin{array}{c}-16\\33 \end{array}\right)+\left(\begin{array}{c}0,5\\-33 \end{array}\right)={{/formula}} | ||
| 25 | c) | ||
| 26 | {{formula}}\left(\begin{array}{c}-1,5\\\frac{1}{3} \end{array}\right)+\left(\begin{array}{c}\sqrt{2}\\\pi\end{array}\right)={{/formula}} | ||
| 27 | d) | ||
| 28 | {{formula}}\left(\begin{array}{c}\frac{1}{2}\sqrt{2}\\5\pi \end{array}\right)-\left(\begin{array}{c}\sqrt{2}\\\pi\end{array}\right)={{/formula}} | ||
| 29 | e) | ||
| 30 | {{formula}}\left(\begin{array}{c}\frac{3}{7}\\5 \end{array}\right)+\left(\begin{array}{c}\frac{5}{7}\\5 \end{array}\right)-\left(\begin{array}{c}\frac{1}{7}\\5 \end{array}\right)={{/formula}} | ||
| 31 | |||
| 32 | f) | ||
| 33 | {{formula}}\left(\begin{array}{c}1\\7\\9 \end{array}\right)+\left(\begin{array}{c}2\\4\\-1 \end{array}\right)={{/formula}} | ||
| 34 | g) | ||
| 35 | {{formula}}\left(\begin{array}{c}100\\71\\92 \end{array}\right)+\left(\begin{array}{c}203\\4\\-119\end{array}\right)={{/formula}} | ||
| 36 | h) | ||
| 37 | {{formula}}\left(\begin{array}{c}12,6\\8,1\\0,3\end{array}\right)-\left(\begin{array}{c}-0,6\\0,9\\\frac{1}{3}\end{array}\right)={{/formula}} | ||
| 38 | i) | ||
| 39 | {{formula}}\left(\begin{array}{c}1\\0,5\\4\end{array}\right)-\left(\begin{array}{c}-1\\0,5\\4\end{array}\right)+\left(\begin{array}{c}-1\\-2\\20\end{array}\right)={{/formula}} | ||
| 40 | {{/aufgabe}} | ||
| 41 | |||
| 42 | {{aufgabe id="Multiplikation eines Vektors mit einer Zahl zeichnerisch" afb="I" kompetenzen="K5" quelle="Torben Würth" cc="BY-SA" zeit="6"}} | ||
| 43 | a) Zeichne ein zweidimensionales Koordinatensystem und ermittle zeichnerisch {{formula}}\vec{a}+\vec{a}=2\vec{a}{{/formula}} mit {{formula}}\vec{a}= \left(\begin{array}{c}1\\3 \end{array}\right){{/formula}} | ||
| 44 | b) Zeichne ein zweidimensionales Koordinatensystem und ermittle zeichnerisch {{formula}}\vec{a}+\vec{a}+\vec{a}=3\vec{a}{{/formula}} mit {{formula}}\vec{a}= \left(\begin{array}{c}-2\\1 \end{array}\right){{/formula}} | ||
| 45 | {{/aufgabe}} | ||
| 46 | |||
| 47 | {{aufgabe id="Gemischte Aufgaben" afb="I" kompetenzen="K5" quelle="Torben Würth" cc="BY-SA" zeit="6"}}a) {{formula}}2\left(\begin{array}{c}1\\3 \end{array}\right)={{/formula}} | ||
| 48 | b) {{formula}}3\left(\begin{array}{c}-2\\1 \end{array}\right)={{/formula}} | ||
| 49 | c) {{formula}}6\left(\begin{array}{c}-1\\6 \end{array}\right)={{/formula}} | ||
| 50 | d) {{formula}}\frac{1}{3}\left(\begin{array}{c}-3\\18 \end{array}\right)={{/formula}} | ||
| 51 | e) {{formula}}2\left(\begin{array}{c}\frac{3}{7}\\5 \end{array}\right)+ 3\left(\begin{array}{c}\frac{5}{7}\\5 \end{array}\right)-4\left(\begin{array}{c}\frac{1}{7}\\5 \end{array}\right)={{/formula}} | ||
| 52 | f){{formula}}-2\left(\begin{array}{c}1\\0,5\\4\end{array}\right)-4\left(\begin{array}{c}-1\\0,5\\4\end{array}\right)+\frac{1}{2}\left(\begin{array}{c}-1\\-2\\20\end{array}\right)={{/formula}}{{/aufgabe}} | ||
| 53 | ~{~{/aufgabe}} |