Difference between revisions of "Selftest: Cross product"
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− | {{ExerciseNavigation|previous=[[Selftest:Dot product|Dot product]]| | + | {{ExerciseNavigation|previous=[[Selftest: Dot product|Dot product]]|chapter=[[Vector algebra]]|article=[[Cross product]]|next=[[Selftest: Introduction to vector algebra|Introduction to vector algebra]]}} |
− | <quiz> | + | <quiz display=simple> |
{'''Please mark the right transforms:''' } | {'''Please mark the right transforms:''' } | ||
+ <math>\vec{\mathbf{a}}\times\vec{\mathbf{b}}= 0 \text{ for } \vec{\mathbf{a}} \upuparrows\vec{\mathbf{b}}</math> | + <math>\vec{\mathbf{a}}\times\vec{\mathbf{b}}= 0 \text{ for } \vec{\mathbf{a}} \upuparrows\vec{\mathbf{b}}</math> | ||
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||The magnitude of the cross product results from the following equation: <math>\vec{\mathbf{a}}\times\vec{\mathbf{b}}=\vec{\mathbf{c}}\text{ with}\left|\vec{\mathbf{c}}\right|= ab\sin\alpha</math>. Here the angle is 180° and the related sine is zero. So the result is 0. | ||The magnitude of the cross product results from the following equation: <math>\vec{\mathbf{a}}\times\vec{\mathbf{b}}=\vec{\mathbf{c}}\text{ with}\left|\vec{\mathbf{c}}\right|= ab\sin\alpha</math>. Here the angle is 180° and the related sine is zero. So the result is 0. | ||
− | {'''Please mark the right transforms: (x,y,z are coordinate axes, a and b are arbitrary''' } | + | {'''Please mark the right transforms: (x,y,z are coordinate axes, a and b are arbitrary)''' } |
+ <math>\vec{\mathbf{b}} \times \vec{\mathbf{a}}=-(\vec{\mathbf{a}}\times \vec{\mathbf{b}})</math> | + <math>\vec{\mathbf{b}} \times \vec{\mathbf{a}}=-(\vec{\mathbf{a}}\times \vec{\mathbf{b}})</math> | ||
+ <math>\vec{\mathbf{y}}\times\vec{\mathbf{x}}=-\vec{\mathbf{z}} </math> | + <math>\vec{\mathbf{y}}\times\vec{\mathbf{x}}=-\vec{\mathbf{z}} </math> | ||
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{ '''The following vectors are given.''' | { '''The following vectors are given.''' | ||
− | [[File: | + | [[File:Vectoralgebra_crossproduct.jpg|300px]] |
− | + | Please mark the correct statements sonsidering the the given vectors. | |
} | } | ||
− | + | + | + The vector <math>\vec{\mathbf{a}}\times\vec{\mathbf{b}}</math> is perpendicular to the plane that is spanned by the vectors <math>\vec{\mathbf{a}}</math> and <math>\vec{\mathbf{b}}</math>. |
− | + | + The magnitude of the cross product equals the area of the parallelogram that is spanned by the vectors <math>\vec{\mathbf{a}}</math> and <math>\vec{\mathbf{b}}</math>. | |
− | + | + The vectors <math>\vec{\mathbf{a}}</math>, <math>\vec{\mathbf{b}}</math> and <math> \vec{\mathbf{a}}\times\vec{\mathbf{b}}</math> form a rectangular coordinate system. So they are arranged as thumb, middle finger and forefinger of the right hand. | |
− | + | ||
</quiz> | </quiz> | ||
[[Category:Selftest]] | [[Category:Selftest]] | ||
[[Category:Vectors]] | [[Category:Vectors]] |
Latest revision as of 10:18, 25 September 2014
← Previous exercise: Dot product | Exercises for chapter Vector algebra | Article: Cross product | Next exercise: Introduction to vector algebra → |