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).
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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
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.