vector


vector
vectorial /vek tawr"ee euhl, -tohr"-/, adj.vectorially, adv.
/vek"teuhr/, n.
1. Math.
a. a quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude. Cf. scalar (def. 4).
b. such a quantity with the additional requirement that such quantities obey the parallelogram law of addition.
c. such a quantity with the additional requirement that such quantities are to transform in a particular way under changes of the coordinate system.
d. any generalization of the above quantities.
2. the direction or course followed by an airplane, missile, or the like.
3. Biol.
a. an insect or other organism that transmits a pathogenic fungus, virus, bacterium, etc.
b. any agent that acts as a carrier or transporter, as a virus or plasmid that conveys a genetically engineered DNA segment into a host cell.
4. Computers. an array of data ordered such that individual items can be located with a single index or subscript.
v.t.
5. Aeron. to guide (an aircraft) in flight by issuing appropriate headings.
6. Aerospace. to change direction of (the thrust of a jet or rocket engine) in order to steer the craft.
[1695-1705; < L: one that conveys, equiv. to vec-, var. s. of vehere to carry + -tor -TOR]

* * *

In mathematics, a quantity characterized by magnitude and direction.

Some physical and geometric quantities, called scalars, can be fully defined by a single number specifying their magnitude in suitable units of measure (e.g., mass in grams, temperature in degrees, time in seconds). Quantities like velocity, force, and displacement must be specified by a magnitude and a direction. These are vectors. A vector quantity can be visualized as an arrow drawn in a specific direction, whose length is equal to the magnitude of the quantity represented. A two-dimensional vector is specified by two coordinates, a three-dimensional vector by three coordinates, and so on. Vector analysis is a branch of mathematics that explores the utility of this type of representation and defines the ways such quantities may be combined. See also vector operations.

* * *

      in mathematics, a quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration. In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs (Gibbs, J Willard) and Oliver Heaviside (Heaviside, Oliver) (of the United States and Britain, respectively) independently developed vector analysis to express the new laws of electromagnetism discovered by the Scottish physicist James Clerk Maxwell (Maxwell, James Clerk). Since that time, vectors have become essential in physics, mechanics, electrical engineering, and other sciences to describe forces mathematically.

      Vectors may be visualized as directed line segments whose lengths are their magnitudes. Since only the magnitude and direction of a vector matter, any directed segment may be replaced by one of the same length and direction but beginning at another point, such as the origin of a coordinate system. Vectors are usually indicated by a boldface letter, such as v. A vector's magnitude, or length, is indicated by |v|, or v, which represents a one-dimensional quantity (such as an ordinary number) known as a scalar. Multiplying a vector by a scalar changes the vector's length but not its direction, except that multiplying by a negative number will reverse the direction of the vector's arrow. For example, multiplying a vector by 1/2 will result in a vector half as long in the same direction, while multiplying a vector by −2 will result in a vector twice as long but pointed in the opposite direction.

 Two vectors can be added or subtracted. For example, to add or subtract vectors v and w graphically (see the diagram—>), move each to the origin and complete the parallelogram formed by the two vectors; v + w is then one diagonal vector of the parallelogram, and v − w is the other diagonal vector.

 There are two different ways of multiplying two vectors together. The cross, or vector, product results in another vector that is denoted by v × w. The cross product magnitude is given by |v × w| = vw sin θ, where θ is the smaller angle between the vectors (with their “tails” placed together). The direction of v × w is perpendicular to both v and w, and its direction can be visualized with the right-hand rule, as shown in the figure—>. The cross product is frequently used to obtain a “normal” (a line perpendicular) to a surface at some point, and it occurs in the calculation of torque and the magnetic force on a moving charged particle.

      The other way of multiplying two vectors together is called a dot product, or sometimes a scalar product because it results in a scalar. The dot product is given by v ∙ w = vw cos θ, where θ is the smaller angle between the vectors. The dot product is used to find the angle between two vectors. (Note that the dot product is zero when the vectors are perpendicular.) A typical physical application is to find the work W performed by a constant force F acting on a moving object d; the work is given by W = Fd cos θ.

      in physics, a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude. Although a vector has magnitude and direction, it does not have position. That is, as long as its length is not changed, a vector is not altered if it is displaced parallel to itself.

      In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars (scalar). For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars.

      To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of combination. One of these is vector addition, written symbolically as A + B = C (vectors are conventionally written as boldface letters). Geometrically, the vector sum can be visualized by placing the tail of vector B at the head of vector A and drawing vector C—starting from the tail of A and ending at the head of B—so that it completes the triangle. If A, B, and C are vectors, it must be possible to perform the same operation and achieve the same result (C) in reverse order, B + A = C. Quantities such as displacement and velocity have this property ( commutative law), but there are quantities (e.g., finite rotations in space) that do not and therefore are not vectors.

      The other rules of vector manipulation are subtraction, multiplication by a scalar, scalar multiplication (also known as the dot product or inner product), vector multiplication (also known as the cross product), and differentiation. There is no operation that corresponds to dividing by a vector. See vector analysis for a description of all of these rules.

      Although vectors are mathematically simple and extremely useful in discussing physics, they were not developed in their modern form until late in the 19th century, when Josiah Willard Gibbs (Gibbs, J Willard) and Oliver Heaviside (Heaviside, Oliver) (of the United States and England, respectively) each applied vector analysis in order to help express the new laws of electromagnetism, proposed by James Clerk Maxwell (Maxwell, James Clerk).

* * *


Universalium. 2010.

Look at other dictionaries:

  • Vector — may refer to: In mathematics * Euclidean vector, a geometric entity endowed with both length and direction, an element of a Euclidean vector space * Coordinate vector, in linear algebra, an explicit representation of an element of any abstract… …   Wikipedia

  • vector — VECTÓR, vectori, s.m. Mărime matematică sau fizică definită printr o valoare numerică, o unitate de măsură, o direcţie şi un punct de aplicaţie (reprezentată grafic printr un segment de dreaptă orientat). ♢ (Adjectival) Rază vectoare. – Din fr.… …   Dicționar Român

  • Vector WX-8 — Vector WX 8 …   Википедия

  • vector — m. microb. Hospedador intermediario que transporta y transmite un microorganismo patógeno productor de enfermedad. Pueden ser mamíferos, artrópodos, etc. También se denomina vehículo. ⊆ genét. Plásmido o cromosoma vírico en cuyo genoma se inserta …   Diccionario médico

  • Vector — Vec tor, n. [L., a bearer, carrier. fr. vehere, vectum, to carry.] 1. Same as {Radius vector}. [1913 Webster] 2. (Math.) A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the… …   The Collaborative International Dictionary of English

  • Vector — steht für in der Informatik ein eindimensionales Array einen Vektorprozessor den Sportwagenhersteller Vector Motors Corporation sowie dessen Fahrzeugmodelle. die Linuxdistribution VectorLinux die Vector Informatik, eine auf Software Tools und… …   Deutsch Wikipedia

  • VECTOR — apud Treb. Pollionem, in Gallienis, c. 12. Quum taurum ingentem in arenam misisset, exîssetque ad eum feriendum vector, neque perductum decies potuisset occidere etc. venator est, sic dictus ex Graeco δ᾿έκτης, quod opuds sit viribus maximis ad… …   Hofmann J. Lexicon universale

  • vector — (Del lat. vector, ōris, que conduce). 1. m. Agente que transporta algo de un lugar a otro. U. t. c. adj.) 2. Bioquím. Fragmento de ácido desoxirribonucleico que puede unir otro fragmento ajeno y transferirlo al genoma de otros organismos. 3. Fil …   Diccionario de la lengua española

  • Vector — (Math.), s. Radius vector …   Pierer's Universal-Lexikon

  • Vector — (Radius vector), »Fahrstrahl«, Leitstrahl; s. Radius und Kegelschnitte; vgl. Vektoranalysis …   Meyers Großes Konversations-Lexikon

  • vector — (n.) quantity having magnitude and direction, 1704, from L. vector one who carries or conveys, carrier, from pp. stem of vehere carry, convey (see VEHICLE (Cf. vehicle)) …   Etymology dictionary


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.