Vector

What is a vector?

In physics, a line segment in space that starts from one point to another is called a vector, that is, it has direction and sense. The function of vectors in physics is to express the so-called vector magnitudes.

The term vector comes from Latin vector, vectoris, whose meaning is 'the one who leads', or 'the one who carries'.

Vectors are represented graphically with an arrow. Likewise, when they must be expressed in a formula, they are represented by a letter surmounted by an arrow.

Example 1:

Example 2:

Vector quantities

Vector quantities are those quantities that, in addition to being represented by a number and a unit, also need to be expressed in space with a direction and a sense, that is, with a vector. This distinguishes them from scalar quantities, which only require one number and one unit. Examples of vector quantities are the following:

  • speed;
  • displacement;
  • acceleration;
  • impulse;
  • force;
  • weight;
  • power;
  • electric field;
  • magnetic field;
  • gravitational field;
  • thermal energy;
  • torque;
  • momentum.

Vector characteristics

The components of the vectors that define their characteristics are the following:

  • Modulus or magnitude: refers to the length or amplitude of the vector or line segment.
  • Direction: refers to the inclination that the vector has with respect to an imaginary horizontal axis, with which it forms an angle.
  • Direction: refers to the orientation of the vector, indicated by the head of the vector arrow.

Types of vectors

  • Null vectors: are those where origin and end coincide and, therefore, the module or magnitude is equal to 0. For example:

  • Unit vectors: are those whose modulus is equal to 1. For example:

  • Fixed vectors: are those that express a point of origin in addition to an extreme, which is determined at a fixed point in space. They are often used, for example, to express the force applied to that point. To represent them, the point of origin is said to be A and the endpoint is B. For example:

  • Parallel vectors: they are located on parallel lines, but they have the same or opposite direction. For instance:

  • Opposite vectors: they are characterized by having the same direction and magnitude, but their sense is opposite. For instance:

  • Concurrent or angular vectors: are those whose lines of action pass through the same point, that is, they intersect. For instance:

  • Free vectors: are those vectors whose application point is indeterminate and, therefore, free. For example:

  • Equipolentes or equal vectors: are those vectors with the same module, direction and sense. For example:

  • Coplanar vectors: are those that are in the same plane. For example:

  • Collinear vectors: their lines of action lie on the same line. For example:

  • Axial vectors or pseudovectors: are those that are linked to the effects of rotation. The direction points to the axis of rotation of the segment. For example:

Vector in mathematics

In mathematics, in the area of ​​vector calculation, vector is an oriented line segment, which depends on a coordinate system, in which a significant number of operations can be carried out, such as addition, subtraction, decomposition, angle between two vectors, etc.

Vector in health

In medicine, a vector is any living and organic being capable of transporting viruses, bacteria, fungi or parasites from an infected being to a healthy one. For example: the mosquito Aedes aegypti It is the vector of dengue and yellow fever, that is, it is responsible for transporting the agent that transmits the disease.

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