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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 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
- Coordinate system
- Helmholtz decomposition (decomposition of a vector field)
- Poloidal–toroidal decomposition
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