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 . A three-dimensional vector for example is
where , and describe the components of the vector in x-, y- and z-direction. For graphical representations arrows are used that show the direction of the vector and whose length equals its magnitude. The magnitude of a vector is defined as
As the presented notation is comparatively sophisticated is often reduced to . The vector has the same magnitude as but is directed opposite. Two or more vectors are called equal if they have the same direction and the same magnitude. The zero vector is a special vector with undefined direction and magnitude zero.