# Vector decomposition

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**Vector decomposition** is the decomposition of a vector of **R**^{n} into several vectors, all linearly independent (in mutually distinct directions in the *n*-dimensional space).

## Vector decomposition in two dimensions

In two dimensions, a vector can be decomposed in many ways. In the Cartesian coordinate system, the vector is decomposed into a portion along the or and the or directions.

One of the most common situations is when given a vector with magnitude and direction (or given in polar form), it can be converted into the sum of two perpendicular vectors (or converted to a Cartesian coordinate). In order to do this it makes use of trigonometry, such as sine and cosine.

## Application in physics

Vector decomposition is used in physics to help adding vectors and hence solve many mechanical problems involving force, work, momentum, etc.

## See also

- Coordinate system
- Helmholtz decomposition (decomposition of a vector field)