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Vector decomposition refers to decomposing a vector of R^{n} into several vectors, each 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 $hat\{x\}$ or $hat\{i\}$ and the $hat\{y\}$ or $hat\{j\}$ directions.## 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

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).

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

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Last updated on Thursday September 04, 2008 at 04:05:25 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Thursday September 04, 2008 at 04:05:25 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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