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It is common to call these tuples vectors, even in contexts where vector-space operations do not apply. More generally, when some data can be represented naturally by vectors, they are often called vectors even when addition and scalar multiplication of vectors are not valid operations on these data. [disputed – discuss] Here are some examples.
Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field ...
In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] [1] A vector space over a field F is a non-empty set V together with a binary operation and a binary function that satisfy the eight axioms listed below. In this context, the elements of V are commonly called vectors, and the elements of F are called ...
The wind triangle graphically represents the relationships among velocity vectors used for air navigation. In air navigation, the wind triangle is a graphical representation of the relationship between aircraft motion and wind. It is used extensively in dead reckoning navigation. The wind triangle is a vector diagram, with three vectors.
When vectors are represented by column vectors, the dot product can be expressed as a matrix product involving a conjugate transpose, denoted with the superscript H: =. In the case of vectors with real components, this definition is the same as in the real case.
Consider n-dimensional vectors that are formed as a list of n scalars, such as the three-dimensional vectors = [] = []. These vectors are said to be scalar multiples of each other, or parallel or collinear , if there is a scalar λ such that x = λ y . {\displaystyle \mathbf {x} =\lambda \mathbf {y} .}
This is an accepted version of this page This is the latest accepted revision, reviewed on 28 January 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 ...
Figure 1: Parallelogram construction for adding vectors. This construction has the same result as moving F 2 so its tail coincides with the head of F 1, and taking the net force as the vector joining the tail of F 1 to the head of F 2. This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth.