Difference between revisions of "Unit vectors"
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|Title=Determination of the unit vector to a given vector | |Title=Determination of the unit vector to a given vector | ||
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− | To the given vector <math>\vec{\mathbf{b}}</math> the corresponding unit vector shall be determined: | + | To the given vector <math>\vec{\mathbf{b}}</math> the corresponding unit vector shall be determined (for detailed information about the handling of arithmetic operations please have a look on the article about [[Simple arithmetic operations|simple arithmetic operations]]): |
:<math> | :<math> | ||
\vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} | \vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} |
Revision as of 11:07, 26 September 2014
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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:
How arithmetic operations like fractions are handled exactly, is described in the article about simple arithmetic operations.
Example: Determination of the unit vector to a given vector
To the given vector the corresponding unit vector shall be determined (for detailed information about the handling of arithmetic operations please have a look on the article about simple arithmetic operations): 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)