Definitions

Vector decomposition

Vector decomposition

Vector decomposition refers to decomposing a vector of Rn 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.

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).

Application in physics

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

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