vector

We explain what a vector is in physics and mathematics, its meaning, types, characteristics and examples. In addition, other meanings of vector.

Vectors can be represented on the Cartesian plane with x, y coordinates.

What is a vector?

In physical Y math, a vector is a segment of a straight line, endowed with a sense, that is, oriented within a two-dimensional or three-dimensional Euclidean plane. Or what is the same: a vector is an element in a space vector.

Vectors make it possible to represent physical quantities endowed not only with intensity, but also with address, as is the case of the force, speed or displacement. This feature of having direction is what distinguishes vector magnitudes from scalars.

Furthermore, a vector can be represented in a Cartesian plane using a set of coordinates (x,Y), or a three-dimensional one (x,Y,z). Vectors are typically represented by an arrow drawn above the symbol used.

Characteristics of a vector

The vectors, represented graphically, have the following characteristics:

  • Direction. Defined as the line on which the vector is drawn, continued infinitely in the space.
  • Modulus or amplitude. The length graph that is equivalent, within a plane, to the magnitude of the vector expressed numerically.
  • Sense. Represented by the head of the arrow that graphically represents the vector, it indicates the locus towards which the vector is directed.
  • Application point. Corresponding to the place or geometric point where the vector begins graphically.
  • Name or denomination. Represented by a letter that accompanies the graphically represented vector, and that coincides with the magnitude that it expresses or with the sum of the starting and ending points of its value.

Sense of a vector

The direction of the vectors is represented graphically by an arrowhead pointing in some direction. This represents which side of the line of action (direction) the vector is heading, that is, where it is pointing.

The sense is extremely important when expressing vector quantities, since it can determine the type of operation or calculation that can be carried out with them.

Types of vectors

Depending on the location of their point of application, vectors are classified into:

  • Free vectors. Those that do not have a particular point of application.
  • Sliding vectors. Those whose application point can be any one along the application line.
  • Fixed or linked vectors. Those that have a single and determined point of application.

However, it is also possible to classify vectors according to other elements, as follows:

  • Angular or concurrent vectors. Those who form angles regarding their lines of action or directions.
  • Opposite vectors. Those that have the same magnitude but the opposite direction.
  • Collinear vectors. Those who share a straight line of action.
  • Parallel vectors. Those whose lines of action are precisely parallel.
  • Coplanar vectors. Those whose lines of action are located on the same plane.

Vector Examples

Vectors allow us to represent the different forces involved in a movement. Physics uses vectors in the Cartesian plane to represent the combination of forces. Vectors allow opposing forces to be represented by pointing out the direction.

Vectors can be added and subtracted from each other.

In the Cartesian plane, vectors allow you to do many other calculations.

Other meanings of "vector"

The term vector is also used in biology, with the sense of "transmission mechanism" of some disease or infectious agent.

For example, the mosquito can be a vector for numerous diseases that necessarily require the bite of this insect to be transmitted to the human being. Vectors unintentionally serve for the infectious agent to mature and spread geographically or populationally.

On the other hand, we speak of a vector also in the field of spatial navigation, such as synonymous of "shuttle", that is, the space launch vehicle that allows other smaller vehicles to reach outer space.

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