Vector decomposition
From Wikipedia, the free encyclopedia
Vector decomposition refers to decomposing a vector of Rn into several vectors, each linearly independent (in mutually distinct directions in the n-dimensional space).
[edit] Vector decomposition in two dimension
In two dimensions, a vector can be decomposed in many ways. In the cartesian system, the vector is decomposed into a portion along the 
or 
and the 
or 
directions.
One of the most common situation is when given a vector with magnitude and direction(or given in polar form), it can be converted into sum of two perpendicular vector(or converted to cartesian coordinate).
[edit] Application in physics
Vector decomposition is used in physics to help adding vectors and hence solve many mechanical problems involving force, work, momentum, etc.
[edit] See also
- coordinate system
- Helmholtz decomposition (decomposition of a vector field)
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