Difference between revisions of "Selftest: Simple arithmetic operations"

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{'''Welche Aussage stimmt?'''}
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{'''Which statement is true?'''}
  
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''(mehrer Antworten sind möglich)''
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''(multiple answers possible)''
  
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- Zur Berechnung des Differenzvektors <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> bildet man zunächst den Vektor <math>-\vec{\mathbf{a}}</math>, indem man bei dem Vektor <math>\vec{\mathbf{a}}</math> die Richtung umkehrt.
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- For the calculation of the difference vector <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> first the vector <math>-\vec{\mathbf{a}}</math> is formed by inverting the direction of <math>\vec{\mathbf{a}}</math>.
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- Zur Berechnung des Differenzvektors <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> bildet man zunächst den Vektor <math>-\vec{\mathbf{b}}</math>, indem man bei dem Vektor <math>\vec{\mathbf{a}}</math> die Richtung umkehrt.
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- For the calculation of the difference vector <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> first the vector <math>-\vec{\mathbf{b}}</math> is formed by inverting the direction of <math>\vec{\mathbf{a}}</math>.
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+ Zur Berechnung des Differenzvektors <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> bildet man zunächst den  Vektor <math>-\vec{\mathbf{b}}</math>, indem man bei dem Vektor <math>\vec{\mathbf{b}}</math> die Richtung umkehrt.
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+ For the calculation of the difference vector <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math> first the vector <math>-\vec{\mathbf{b}}</math>is formed by inverting the direction of <math>\vec{\mathbf{b}}</math>.
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||[[Bild:Vektorrechnung Vektoraddition und -subtraktion.jpg|300px|thumb|left|Die Vektorsubtraktion]] Die Vektorsubtraktion lässt sich auf die Vektoraddition zurückführen, da <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}})</math> gilt. Weitere Erklärung siehe [[Einfache Rechenoperationen mit Vektoren]]  
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||[[File:Vectoralgebra_addition_substraction.png|300px|left|Vector substraction]] The substraction of vectors can be traced back to vector addition because <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}})</math>. Further information: see [[Simple arithmetic operations]]
  
  

Revision as of 16:07, 23 May 2014

← Previous exercise: Unit vector Exercises for chapter {{{chapter}}} | Article: Vector algebra Next exercise: Dot product →
Point added for a correct answer:  
Points for a wrong answer:
Ignore the questions' coefficients:

1. Which of the following vectors forms the sum of \vec{\mathbf{a}} and \vec{\mathbf{b}}?

Vektorrechnung Aufgabe6.1.png


\begin{pmatrix} 0 \\ 6 \end{pmatrix}
\begin{pmatrix} 2 \\ 3 \end{pmatrix}
\begin{pmatrix} 5 \\ 0 \end{pmatrix}
\begin{pmatrix} -2 \\ 3 \end{pmatrix}
→The x-components of the two vectors cancel each other. Therefore the sum vector only has an y-component unequal zero. The length is the sum of the two y-components. Further information: see Simple arithmetic operations

2. Which of the following vectors forms the sum of \vec{\mathbf{a}} and \vec{\mathbf{b}}?

Vektorrechnung Aufgabe6.2.png


\begin{pmatrix} -5 \\ 6 \end{pmatrix}
\begin{pmatrix} -2 \\ 0 \end{pmatrix}
\begin{pmatrix} 0 \\ -3 \end{pmatrix}
\begin{pmatrix} -6 \\ 5 \end{pmatrix}
→Vector \vec{\mathbf{a}} only has an x-component, vector \vec{\mathbf{b}} in contrast only has a y-component. The resulting vector consists of the x-component of \vec{\mathbf{a}} and the y-component of \vec{\mathbf{b}}. Further information: see Simple arithmetic operations

3. Which of the following vectors forms the sum of \vec{\mathbf{a}} and \vec{\mathbf{b}}?

Vektorrechnung Aufgabe6.3.png


\begin{pmatrix} 0 \\ 6 \end{pmatrix}
\begin{pmatrix} 2 \\ 3 \end{pmatrix}
\begin{pmatrix} 3 \\ 4 \end{pmatrix}
\begin{pmatrix} -4 \\ 3 \end{pmatrix}
→The x-component of vector \vec{\mathbf{a}} is directed opposite to the x-component of vector \vec{\mathbf{b}}. So the x-components are substracted. The y-components are added as usual. Further information: see Simple arithmetic operations

4. Which of the following vectors forms the substraction \vec{\mathbf{a}}-\vec{\mathbf{b}}?

Vektorrechnung Aufgabe7.1.png


\begin{pmatrix} 0 \\ -6 \end{pmatrix}
\begin{pmatrix} 7 \\ -3 \end{pmatrix}
\begin{pmatrix} 0 \\ 6 \end{pmatrix}
\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}
→Because the x-components are equal, the resulting x-component is zero. The y-component of the resulting vector is the substraction of the y-components. Further information: see Simple arithmetic operations

5. Which of the following vectors forms the substraction \vec{\mathbf{a}}-\vec{\mathbf{b}}?

Vektorrechnung Aufgabe7.2.png


\begin{pmatrix} 3 \\ 0 \end{pmatrix}
\begin{pmatrix} -2 \\ -3 \end{pmatrix}
\begin{pmatrix} 4 \\ -2 \end{pmatrix}
\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}
→The substraction of vectors can be traced back to vector addition because \vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}}). Further information: see Simple arithmetic operations
Vector subtraction

6. Which of the following vectors forms the substraction \vec{\mathbf{a}}-\vec{\mathbf{b}}?

Vektorrechnung Aufgabe7.3.png


\begin{pmatrix} 0 \\ -6 \end{pmatrix}
\begin{pmatrix} 3 \\ -3 \end{pmatrix}
\begin{pmatrix} 0 \\ 8 \end{pmatrix}
\begin{pmatrix} -2,5 \\ 0,5 \end{pmatrix}
→Because the x-components are equal, the resulting x-component is zero. The y-component of the resulting vector is the substraction of the y-components. Further information: see Simple arithmetic operations

7. Which statement is true?

For the calculation of the difference vector \vec{\mathbf{a}}-\vec{\mathbf{b}} first the vector -\vec{\mathbf{a}} is formed by inverting the direction of \vec{\mathbf{a}}.
For the calculation of the difference vector \vec{\mathbf{a}}-\vec{\mathbf{b}} first the vector -\vec{\mathbf{b}} is formed by inverting the direction of \vec{\mathbf{a}}.
For the calculation of the difference vector \vec{\mathbf{a}}-\vec{\mathbf{b}} first the vector -\vec{\mathbf{b}}is formed by inverting the direction of \vec{\mathbf{b}}.
→
Vector substraction
The substraction of vectors can be traced back to vector addition because \vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}}). Further information: see Simple arithmetic operations

8. Lückentext:

Fügen Sie folgende Wörter ein und achten Sie dabei auf Groß- und Kleinschreibung:

negative Zahl, gleicher Richtung, Nullvektor, Faktor

Multipliziert man einen Vektor \vec{\mathbf{a}} mit einer positiven reellen Zahl p, entsteht ein Vektor\vec{\mathbf{a}}p mit und verändertem Betrag, der sich um den {p} geändert hat. Erhält der Vektor \vec{\mathbf{a}} durch die Multiplikation eine entgegengesetzte Richtung, so handelt es sich um eine . Für den Sonderfall p=0 erhält man einen .

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