Vector Calculus Notation

Mathematical notation is designed to create the correct ideas in the mind of the reader. It is deliberately ambiguous and incomplete; indeed, it is almost meaningless to all other readers.
-- Poppelier, Herwijnen and Rowley, "Standard dtd's and scientific publishing"

As the following table demonstrates, the notations used in vector calculus are myriad. Indeed, this table is not exhaustive.

For the sake of uniformity, these pages will in general use bold letters for vectors and unit vectors, such as v for a vector and i for a unit vector.

Symbol	Definition
	N-tuple of real numbers
	Space of all N-tuples
	Component-wise N-tuple addition
	Scalar multiplication of an N-tuple
	The origin
	the line segment between P and Q
	the line through P and Q
	A vector variable
	The zero vector
	The magnitude of a vector variable
	Displacement vector from P1 to P2
	Unit vector in the direction of the positive x-axis
	Unit vector in the direction of the positive y-axis
	Unit vector in the direction of the positive z-axis
	Vector addition
	Vector negatition
	Scalar multiplication of a vector
	Geometric definition of dot product
	Algebraic definition of dot product (N=3)
	Cross product
	Distance from z-axis in cylindrical coordinates