
related topics 
{math, number, function} 
{math, energy, light} 
{car, race, vehicle} 
{line, north, south} 
{ship, engine, design} 

In elementary mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric^{[1]} or spatial vector,^{[2]} or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B,^{[3]} and denoted by More formally, a Euclidean vector is any element of a Euclidean vector space, i.e. a vector space that has a Euclidean norm. A Euclidean vector space is automatically a type of normed linear space and a type of inner product space.
A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".^{[4]} The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.
Vectors play an important role in physics: velocity and acceleration of a moving object and forces acting on it are all described by vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (such as position or displacement), their magnitude and direction can be still represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vectorlike objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.
Contents
Full article ▸


related documents 
Discrete Fourier transform 
Clifford algebra 
Polynomial 
Floating point 
Generic programming 
Group (mathematics) 
Ordinal number 
Quaternion 
Vienna Development Method 
Algorithm 
Regular expression 
Common Lisp 
Eiffel (programming language) 
Surreal number 
Emmy Noether 
Prime number 
Singular value decomposition 
Radix sort 
Complex number 
Mathematical logic 
Derivative 
Natural deduction 
Lisp (programming language) 
Propositional calculus 
Number 
Smalltalk 
C (programming language) 
Fourier transform 
History of mathematics 
Mandelbrot set 
