The Elements of a vector Are the address, the distance and the module. In mathematics, physics and engineering, a vector is a geometric object that has a magnitude (or length) and direction. According to vector algebra, vectors can be added to other vectors.
Frequently, a vector is represented by a line segment with a defined direction, or graphically represented as an arrow, connecting an initial point A with an endpoint B, denoted by AB.
A vector is what is needed to bring point A to point B. Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can be described with vectors.
Many other physical qualities can be thought of as vectors. The mathematical representation of a physical vector depends on the coordinate system used to describe it.
There are several kinds of vectors, among them we can find the sliding vectors, the collinear vectors, the concurrent vectors, the position vectors, the free vectors, the parallel vectors and the coplanar vectors, among others.
Elements of a vector
Mainly a vector has three elements: the direction, the sense, and the module.
Address
A vector is an entity having magnitude and direction. Examples of vectors include displacement, velocity, acceleration, and force.
To describe one of these vector quantities, it is necessary to find the magnitude and direction.
For example, if the velocity of an object is 25 meters per second, then the velocity description of the object is incomplete, since the object may be moving at 25 meters per second to the south, or 25 meters per second to the north, or 25 meters per second to the southeast.
In order to fully describe the speed of an object, both must be defined: both the magnitude of 25 meters per second, and the direction, for example to the south.
For such descriptions of vector quantities to be useful, it is important that everyone agrees on how the object's address is described.
Most people are accustomed to the idea that a map refers to the east direction if one looks to the right. But this is a mere convention that map makers have used for years so everyone can agree.
So what is the direction of a vector quantity that is not directed north or east if not somewhere between north and east? For these cases it is important that there is some convention to describe the direction of said vector.
This convention is referred to as the CCW. Using this convention we can describe the direction of any vector in terms of its angle of rotation to the left.
Using this convention, the north direction would be at 90 °, since if a vector is pointing east it would have to be rotated 90 ° in the left direction to reach the north point.
Also, the western direction would be located at 180 °, since a vector pointing west would have to be rotated 180 ° to the left to point to the west point.
In other words, the direction of a vector will be represented by a line contained in the vector or any line parallel to it,
It will be determined by the angle formed between the vector and any other reference line. That is, the direction of the line in the vector or some line parallel to it is the direction of the vector.
Sense
The vector sense refers to the element that describes how point A goes to the B end:
The direction of a vector is specified by the order of two points in a line parallel to the vector, as opposed to the direction of the vector which is specified by the relation between the vector and any reference line and / or plane.
Both orientation and direction determine the direction of a vector. Orientation tells what angle the vector is, and the direction tells where it is pointing.
The direction of the vector only establishes the angle that makes a vector with its horizontal axis, but that can create ambiguity since the arrow can point in two opposite directions and equal to realize the same angle.
The meaning clarifies this ambiguity and indicates where the arrow is pointing or where the vector is headed.
Somehow the meaning tells us the order in which to read the vector. Indicates where the vector begins and ends.
Module
The modulus or amplitude of a vector can be defined as the length of segment AB. The module can be represented by a length that is proportional to the value of the vector. The modulus of a vector will always be zero, or in some cases a positive number.
In mathematics, the vector will be defined by its Euclidean distance (modulus), direction and direction.
The Euclidean distance or Euclidean distance, is the 'ordinary' distance in a straight line between two points located in a Euclidean space. With this distance, the Euclidean space becomes metric space.
A Euclidean distance between two points, for example P and Q, is the distance between the line segment connecting them:
The position of a point in a Euclidean space n is a vector. Thus, P and Q are vectors, starting from the origin of the space and its points indicating two points.
The Euclidean norm, magnitude, or Euclidean distance of a vector measures the length of said vector.
References
- Vector direction. Retrieved from physicsclassroom.com.
- What is the sense of a vector? Retrieved from physics.stackexchange.com.
- What is the difference between direction, sense, and orientation? Retrieved from math.stackexchange.com.
- Euclidean distance. Retrieved from wikipedia.org.