Difference between revisions of "Selftest: Simple arithmetic operations"
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− | {{ExerciseNavigation|previous=[[Selftest:Unit vector|Unit vector]]| | + | {{ExerciseNavigation|previous=[[Selftest: Unit vector|Unit vector]]|chapter=[[Vector algebra]]|article=[[Simple arithmetic operations]]|next=[[Selftest: Dot product|Dot product]]}} |
− | <quiz> | + | <quiz display=simple> |
− | {''' | + | {'''Which of the following vectors forms the sum of <math>\vec{\mathbf{a}}</math> and <math>\vec{\mathbf{b}}</math>?''' |
− | [[File:Vektorrechnung_Aufgabe6.1.png|200px | + | [[File:Vektorrechnung_Aufgabe6.1.png|200px|left]] |
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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- <math>\begin{pmatrix} 5 \\ 0 \end{pmatrix}</math> | - <math>\begin{pmatrix} 5 \\ 0 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -2 \\ 3 \end{pmatrix}</math> | - <math>\begin{pmatrix} -2 \\ 3 \end{pmatrix}</math> | ||
− | || | + | ||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]] |
</div> | </div> | ||
− | + | {'''Which of the following vectors forms the sum of <math>\vec{\mathbf{a}}</math> and <math>\vec{\mathbf{b}}</math>?''' | |
− | {''' | + | [[File:Vektorrechnung_Aufgabe6.2.png|200px|left]] |
− | [[File:Vektorrechnung_Aufgabe6.2.png|200px | ||
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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- <math>\begin{pmatrix} 0 \\ -3 \end{pmatrix}</math> | - <math>\begin{pmatrix} 0 \\ -3 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -6 \\ 5 \end{pmatrix}</math> | - <math>\begin{pmatrix} -6 \\ 5 \end{pmatrix}</math> | ||
− | || | + | ||Vector <math>\vec{\mathbf{a}}</math> only has an x-component, vector <math>\vec{\mathbf{b}}</math> in contrast only has a y-component. The resulting vector consists of the x-component of <math>\vec{\mathbf{a}}</math> and the y-component of <math>\vec{\mathbf{b}}</math>. Further information: see [[Simple arithmetic operations]] |
</div> | </div> | ||
− | {''' | + | {'''Which of the following vectors forms the sum of <math>\vec{\mathbf{a}}</math> and <math>\vec{\mathbf{b}}</math>?''' |
− | [[File:Vektorrechnung_Aufgabe6.3.png|200px | + | [[File:Vektorrechnung_Aufgabe6.3.png|200px|left]] |
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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+ <math>\begin{pmatrix} 3 \\ 4 \end{pmatrix}</math> | + <math>\begin{pmatrix} 3 \\ 4 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -4 \\ 3 \end{pmatrix}</math> | - <math>\begin{pmatrix} -4 \\ 3 \end{pmatrix}</math> | ||
− | || | + | ||The x-component of vector <math>\vec{\mathbf{a}}</math> is directed opposite to the x-component of vector <math>\vec{\mathbf{b}}</math>. So the x-components are substracted. The y-components are added as usual. Further information: see [[Simple arithmetic operations]] |
</div> | </div> | ||
− | {''' | + | {'''Which of the following vectors forms the substraction <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math>?''' |
− | [[File:Vektorrechnung_Aufgabe7.1.png|200px | + | [[File:Vektorrechnung_Aufgabe7.1.png|200px|left]] |
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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- <math>\begin{pmatrix} 0 \\ 6 \end{pmatrix}</math> | - <math>\begin{pmatrix} 0 \\ 6 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}</math> | - <math>\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}</math> | ||
− | || | + | ||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]] |
</div> | </div> | ||
− | {''' | + | {'''Which of the following vectors forms the substraction <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math>?''' |
− | [[File:Vektorrechnung_Aufgabe7.2.png|200px | + | [[File:Vektorrechnung_Aufgabe7.2.png|200px|left]] |
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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+ <math>\begin{pmatrix} 4 \\ -2 \end{pmatrix}</math> | + <math>\begin{pmatrix} 4 \\ -2 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}</math> | - <math>\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}</math> | ||
− | || | + | ||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]] [[File:Vectoralgebra_addition_substraction.png|300px|left|Vector subtraction]] |
</div> | </div> | ||
− | {''' | + | {'''Which of the following vectors forms the substraction <math>\vec{\mathbf{a}}-\vec{\mathbf{b}}</math>?''' |
− | [[File:Vektorrechnung_Aufgabe7.3.png|200px | + | [[File:Vektorrechnung_Aufgabe7.3.png|200px|left]] |
<div style="float:left;"> | <div style="float:left;"> | ||
<br style="clear:both;" /> | <br style="clear:both;" /> | ||
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- <math>\begin{pmatrix} 0 \\ 8 \end{pmatrix}</math> | - <math>\begin{pmatrix} 0 \\ 8 \end{pmatrix}</math> | ||
- <math>\begin{pmatrix} -2,5 \\ 0,5 \end{pmatrix}</math> | - <math>\begin{pmatrix} -2,5 \\ 0,5 \end{pmatrix}</math> | ||
− | || | + | ||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]] |
</div> | </div> | ||
− | {''' | + | {'''Which statement is true?'''} |
− | ''( | + | ''(multiple answers possible)'' |
− | - | + | - 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>. |
− | - | + | - 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>. |
− | + | + | + 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>. |
− | || | + | ||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]] [[File:Vectoralgebra_addition_substraction.png|300px|left|Vector substraction]] |
− | {''' | + | {'''Fill-in-the-blank text:''' |
− | + | Fill in the following words: | |
− | ''negative | + | ''negative value, same direction, zero vector, factor'' |
| type="{}" } | | type="{}" } | ||
− | + | Multiplying a vector <math>\vec{\mathbf{a}}</math> by a real value ''p'' results in a vector <math>\vec{\mathbf{a}}_p</math> with { same direction } and different magnitude. The magnitude changes with { factor } <math>{p}</math>. If the resulting vector <math>\vec{\mathbf{a}}_p</math> has an oppsite direction, ''p'' is a { negative value }. The special case ''p=0'' results in a { zero vector }. | |
</quiz> | </quiz> | ||
Latest revision as of 10:57, 30 November 2014
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