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.
The following subarticles describe the unit vector and the basic arithmetic operations including dot and cross product:
Example: Movement of a flying object
Consider a flying object at time . This object not only has a current velocity but also a direction of motion. Thus the velocity of the object is a vector . The corresponding distance then arises out of the product of the velocity vector and the time: |