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There are two lists of mathematical identities related to vectors: Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
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 .
This article uses the convention that vectors are denoted in a bold font (e.g. a 1), and scalars are written in normal font (e.g. a 1). The dot product of vectors a and b is written as a ⋅ b {\displaystyle \mathbf {a} \cdot \mathbf {b} } , the norm of a is written ‖ a ‖, the angle between a and b is denoted θ .
In order to calculate with vectors, the graphical representation may be too cumbersome. Vectors in an n-dimensional Euclidean space can be represented as coordinate vectors in a Cartesian coordinate system. The endpoint of a vector can be identified with an ordered list of n real numbers (n-tuple).
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 February 2025. Computer graphics images defined by points, lines and curves This article is about computer illustration. For other uses, see Vector graphics (disambiguation). Example showing comparison of vector graphics and raster graphics upon magnification Vector graphics are a form of computer ...
This is a list of graphical methods with a mathematical basis. Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization . There is also a list of computer graphics and descriptive geometry topics .
For a vector to represent a geometric object, it must be possible to describe how it looks in any other coordinate system. That is to say, the components of the vectors will transform in a certain way in passing from one coordinate system to another. A simple illustrative case is that of a Euclidean vector.
They form a set of mutually orthogonal unit vectors, typically referred to as a standard basis in linear algebra. They are often denoted using common vector notation (e.g., x or x → {\displaystyle {\vec {x}}} ) rather than standard unit vector notation (e.g., x̂ ).