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Mathematical Representation of Vectors

Vectors can be represented in terms of unit vectors.  There is one unit vector for each dimension in the space. A unit vector is a vector of magnitude 1. The direction can be any arbitrary direction as long as the magnitude is 1. A unit vector is written with a caret on the top of the symbol, such as .

In the top figure at the left, the unit vectors along the three Cartesian axis of the three dimensional space are represented. Also, their definition in terms of the vector-matrix notation are given. These unit vectors are used to represent any arbitrary vector on this space, for example: . The previous expression is call a linear combination of the unit vectors.  Similarly, the bottom draw contain these unit vectors for the case of two dimensional space.

 

 

 

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by Luis F. Sez, Ph. D.    Comments and Suggestions: LSaez@dallaswinwin.com