Difference between revisions of "Vector algebra"
From Robotics
Line 2: | Line 2: | ||
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
← Back: Table of contents | Overview: Vector algebra | Next: Unit vectors → |
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
, 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