A vector is a set of numbers , ..., that transform as

(1) |

A vector is uniquely specified by giving its Divergence and Curl within a region and its normal component over the boundary, a result known as Helmholtz's Theorem (Arfken 1985, p. 79). A vector from a point to a point is denoted , and a vector may be denoted , or more commonly, .

A vector with unit length is called a Unit Vector and is denoted with a Hat. An arbitrary vector may be
converted to a Unit Vector by dividing by its Norm, i.e.,

(2) |

Let be the Unit Vector defined by

(3) |

(4) | |||

(5) | |||

(6) | |||

(7) | |||

(8) | |||

(9) | |||

(10) | |||

(11) | |||

(12) | |||

(13) |

and

(14) |

**References**

Arfken, G. ``Vector Analysis.'' Ch. 1 in *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL:
Academic Press, pp. 1-84, 1985.

Aris, R. *Vectors, Tensors, and the Basic Equations of Fluid Mechanics.* New York: Dover, 1989.

Crowe, M. J. *A History of Vector Analysis: The Evolution of the Idea of a Vectorial System.* New York: Dover, 1985.

Gibbs, J. W. and Wilson, E. B.
*Vector Analysis: A Text-Book for the Use of Students of Mathematics and Physics, Founded Upon the Lectures of J. Willard Gibbs.*
New York: Dover, 1960.

Marsden, J. E. and Tromba, A. J. *Vector Calculus, 4th ed.* New York: W. H. Freeman, 1996.

Morse, P. M. and Feshbach, H. ``Vector and Tensor Formalism.'' §1.5 in
*Methods of Theoretical Physics, Part I.* New York: McGraw-Hill, pp. 44-54, 1953.

Schey, H. M. *Div, Grad, Curl, and All That: An Informal Text on Vector Calculus.* New York: Norton, 1973.

Schwartz, M.; Green, S.; and Rutledge, W. A. *Vector Analysis with Applications to Geometry and Physics.*
New York: Harper Brothers, 1960.

Spiegel, M. R. *Theory and Problems of Vector Analysis.* New York: Schaum, 1959.

© 1996-9

1999-05-26