# Vector decomposition

{{ safesubst:#invoke:Unsubst||$N=Merge to |date=__DATE__ |$B= Template:MboxTemplate:DMCTemplate:Merge partner }} Template:Unreferenced stub Vector decomposition is the decomposition of a vector of Rn 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 ${\displaystyle {\hat {x}}}$ or ${\displaystyle {\hat {i}}}$ and the ${\displaystyle {\hat {y}}}$ or ${\displaystyle {\hat {j}}}$ 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.