Vector algebra

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Overview: Vector algebra

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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 $\vec{\mathbf{a}}$. A three-dimensional vector for example is

$\vec{\mathbf{a}}= \left[\begin{array}{cccc} a_x\\ a_y\\ a_z \end{array}\right] where <math>a_x$, $a_y$ and $a_z$ 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

1. Unit vectors
2. Simple arithmetic operations
3. Dot product
4. Cross product