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In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions. Every bounded surface in three dimensions can be associated with a unique area vector called its vector area .
Special cases are called the real line R 1, the real coordinate plane R 2, and the real coordinate three-dimensional space R 3. With component-wise addition and scalar multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the ...
A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented. In mathematics , orientability is a broader notion that, in two dimensions, allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left ...
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.
geometry corresponds to an experimental reality geometry is a mathematical truth all geometric properties of the space follow from the axioms axioms of a space need not determine all geometric properties geometry is an autonomous and living science classical geometry is a universal language of mathematics space is three-dimensional
The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field. Vector spaces generalize ...
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .