Difference between revisions of "Unit vectors"
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{{Exercise|Selftest: Unit vector}} | {{Exercise|Selftest: Unit vector}} | ||
− | A unit vector is a vector with magnitude 1. The unit vector to a given vector <math>\vec{\mathbf{a}}</math> can be | + | A unit vector is a vector with magnitude 1. The unit vector to a given vector <math>\vec{\mathbf{a}}</math> can be determined by dividing the given vector by its magnitude <math>|\vec{\mathbf{a}}|</math>: |
[[File:unitvector.png|right|300px]] | [[File:unitvector.png|right|300px]] | ||
:<math> | :<math> |
Revision as of 16:43, 25 September 2014
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There are exercises as selftest for this article. |
A unit vector is a vector with magnitude 1. The unit vector to a given vector can be determined by dividing the given vector by its magnitude :
The vector has the magnitude 1 (so ) and is pointed to the direction of . So every vector can be described by its magnitude (so a scalar value) and the corresponding unit vector. Therefore can also be written as follows:
Example: Determination of the unit vector to a given vector
To the given vector the corresponding unit vector shall be determined: The calculation of the magnitude shows thats it equals 1 indeed: |
Literature
- Manfred Albach, Grundlagen der Elektrotechnik 1: Erfahrungssätze, Bauelemente, Gleichstromschaltungen, 3. Edition (Pearson Studium, 2011)