Difference between revisions of "Unit vectors"
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\vec{\textbf{a}} = \frac{\vec{\textbf{a}}}{|\vec{\textbf{a}}|} |\vec{\textbf{a}}| = \vec{\textbf{e}}_{a} |\vec{\textbf{a}}| | \vec{\textbf{a}} = \frac{\vec{\textbf{a}}}{|\vec{\textbf{a}}|} |\vec{\textbf{a}}| = \vec{\textbf{e}}_{a} |\vec{\textbf{a}}| | ||
</math><br/> | </math><br/> | ||
− | How arithmetic operations like fractions are handled exactly, is described in the article about [[Simple arithmetic operations|simple arithmetic operations]]. | + | How arithmetic operations like fractions are handled exactly, is described in the article about [[Simple arithmetic operations|simple arithmetic operations]]. |
− | {{ | + | {{ExampleMatlab |
|Title=Determination of the unit vector to a given vector | |Title=Determination of the unit vector to a given vector | ||
+ | |Matlab=[[MATLAB: Unit vectors|see MATLAB code]] | ||
|Contents= | |Contents= | ||
− | To the given vector <math>\vec{\mathbf{b}}</math> the corresponding unit vector shall be determined: | + | |
+ | ''Hint: For detailed information about the handling of arithmetic operations please have a look on the article about [[Simple arithmetic operations|simple arithmetic operations]]'' | ||
+ | |||
+ | To the given vector <math>\vec{\mathbf{b}}</math> the corresponding unit vector shall be determined:<br/> | ||
:<math> | :<math> | ||
\vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} | \vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} |
Latest revision as of 18:02, 13 November 2015
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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.
Hint: For detailed information about the handling of arithmetic operations please have a look on the article about simple arithmetic operations 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)