Difference between revisions of "Vector algebra"
From Robotics
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This article gives a brief explanation of vectors and vector algebra. <br/> | This article gives a brief explanation of vectors and vector algebra. <br/> | ||
A scalar value is just a numeric value. In contrast thereto, a vectorial value has a direction. Examples for vectors are all forces and the velocity, which is directed to the driving direction.<br/> | A scalar value is just a numeric value. In contrast thereto, a vectorial value has a direction. Examples for vectors are all forces and the velocity, which is directed to the driving direction.<br/> | ||
| − | Vectors are usually denoted with an arrow, for example <math>\vec{\mathbf{a}}</math>. For graphical representations arrows are used that show the direction of the vector and whose length equals its magnitude. The magnitude of a vector | + | Vectors are usually denoted with an arrow, for example <math>\vec{\mathbf{a}}</math>. A three-dimensional vector for example is<br/><br/> |
| + | <math>\vec{\mathbf{a}}= | ||
| + | \left[\begin{array}{cccc} | ||
| + | a_x\\ | ||
| + | a_y\\ | ||
| + | a_z | ||
| + | \end{array}\right] | ||
| + | where <math>a_x</math>, <math>a_y</math> and <math>a_z</math> describe the components of the vector in x-, y- and z-direction. | ||
| + | </math> | ||
| + | |||
| + | For graphical representations arrows are used that show the direction of the vector and whose length equals its magnitude. The magnitude of a vector | ||
# [[Unit vectors]] | # [[Unit vectors]] | ||
Revision as of 15:08, 14 May 2014
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This article gives a brief explanation of vectors and vector algebra.
A scalar value is just a numeric value. In contrast thereto, a vectorial value has a direction. Examples for vectors are all forces and the velocity, which is directed to the driving direction.
Vectors are usually denoted with an arrow, for example 
. A three-dimensional vector for example is
![\vec{\mathbf{a}}=
\left[\begin{array}{cccc}
a_x\\
a_y\\
a_z
\end{array}\right]
where <math>a_x](/wiki/robotics/images/math/3/8/4/3841881c8f592e63dfa432ff2d572b50.png)
, 
and 
describe the components of the vector in x-, y- and z-direction.
</math>
For graphical representations arrows are used that show the direction of the vector and whose length equals its magnitude. The magnitude of a vector
