radial and transverse components

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When a point P has polar coordinates (r, θ), the vectors er and eθ are defined by er=i cos θ+j sin θ and eθ =−i sin θ+j cos θ, where i and j are unit vectors in the directions of the positive x- and y-axes. Then er is a unit vector along OP in the direction of increasing r, and eθ is a unit vector perpendicular to this in the direction of increasing θ. Any vector v can be written in terms of its components in the directions of er and eθ. Thus v=v1er+v2eθ, where v1=v · er and v2=v · eθ. The component v1 is the radial component, and the component v2 is the transverse component.

Subjects: Mathematics.

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