(c) Dr Paul Kinsler. [Acknowledgements & Feedback]

This is part of an information maze -- see the index-file for the full picture.

Vectors

A vector is an arrow that points in a particular direction. In the three-dimensional world, the direction an object is travelling can be indicated by the orientation of the arrow; while its speed can be indicated by the length of the arrow. An N-dimensional vector can be represented by N numbers, each of which refers to the length of the arrow along one of the N coordinate axes describing the space.

There are different sorts of vector quantities, which, although they look the same, transform differently when you change the coordinate axes around. Firstly, there are polar vectors, whose components change sign (i.e. plus to minus, minus to plus) when the coordinate axes are reversed. Quantities like acceleration, velocity, force, and electro-magnetic-fields are represented by polar vectors. Secondly, there are psuedo vectors (or axial vectors), which involve the orientation of an axis in space. Examples of quantities represented by psuedo vectors are angular-velocity, vector-area, and magnetic flux density -- and their dimensions involve length to an even power.

There are three ways of doing algebra with vectors: vector-sum, vector-scalar-product, and vector-cross-product.

MATHS:

XINDEX: velocity, momentum, angular-velocity, angular-momentum, acceleration, index-file.

20000205 19991107 (c) Paul Kinsler

XKEYWORD: vector

Email Feedback: Dr.Paul.Kinsler@physics.org

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