A vector if we are going to etymologically study the word means driving or letting it drive, meaning then that it is a means by which something must be achieved. However, to be sure let’s know what is a vector, definition, meaning and concept.
Vector is the partition of a line that goes in one direction in a straight line in space, into several parts representing multiple paths always in one direction, regardless of whether there is only one or many of them appear in the corresponding place.
If we talk about physics, the vector is responsible for representing the speed of a body or the force that is exerted on that same body, as well as the different directions to which it can go if an impulse is applied to it that generates the path of said body.
Likewise, this type of vector is represented through icons or physical forms called arrows, putting them in the direction of what they are going to represent, for this reason the vector is the way in which you represent any type of magnitude.
- The origin or initial point of the vector.
- Application point.
- The module or size of the vector.
- Final point or endpoint of the vector.
- Direction.
- Sense.
- Orientation.
Instructions
A vector is that figure that has the particularity of having an origin from where it starts until it ends at a point which will represent its arrival, obtaining the possibility of establishing the exact point of arrival of the magnitude to be measured by the vector.
It is important to take into consideration that the vector represents a series of spaces that will determine the size taking into account the origin and the end to which it will reach, maintaining the possibility of finding a point where they converge.
This is how vectors work
- The origin of a vector is the point where it starts and will reveal the possibility of establishing it as the beginning of the drawing, that is, by giving it a value of 0, to start the work and then continue in any direction.
- The point of application of a vector where it settles or a point of support that offers the possibility of establishing a force that will produce the necessary energy to start the vector on its journey towards its final end.
- The module of a vector represents its length or size, determining the calculation from the beginning of the vector to its end, taking into consideration the possibility of having exact measurements to know its length.
- The end of a vector is given by the end of it, having as its starting point the beginning or initial point and ending at the end point which determines how far it can go or what length it has.
- Direction has the power to say to which point of the plane the starting point or vector is directed, having the directions up, down, right, left, among other directions that the arrow seeks to reach the end or end point.
- The vector takes the direction in its line that comes to be represented by an arrow, although it also depends on the “reference axis”, this being the main reference for the vector to take a direction itself.
- The vector will also determine the exact direction of where the arrow will point, that is, it will be influenced by the tip of the vector whose drawing ends in an arrowhead, located at the end of it.
- If we determine the unification of the sense with the direction, then we are before the orientation that the vector must take, since these two concepts can offer a certain value to give norm or regulation to the entire vector.
- In order to represent the start or start point and the end or end point of a vector, letters in lowercase or uppercase are generally assigned depending on the person who makes use of it to represent an image on a plane.
- Apart from the use of these two letters, regardless of whether it is in lowercase or uppercase, an arrow is usually placed above the letters that identifies that it is a vector with the characters indicated above.
- An example of this can be found in: AB CD.
- When a vector is drawn on a plan, two components that are generally identified by the letters X and Y must be taken into account, thus determining their location within the same plane that is called Cartesian.
- The coordinates of a vector come to represent also be defined by points that lead to any digit but in this case a three-dimensional image is used for the number of digits it handles and with the use of coordinates with the letters X, Z and Y
- When it comes to projecting the image of a vector on the plane using any other type of letters, the vectors follow the number indicated by each one without having to look at anything else. An example of this is if X is 2 and Y is 5.
- When adding two vectors, mathematics is applied, obtaining the main vector which will give the final result if we carry out the addition operation of the two digits that represent each of the vectors.
- Vectors can also be classified by types and these are: Coplanar: they are those found in the same place in two different coordinates; Non-coplanar: they are not found together in the same place, and there may be more than two vectors; Free: they are those who are pointing in various directions without having a point to which to point; Collinear: they are those that have the same tracking line, that is, they are directed in the same direction; Angular: they cross each other at the starting point in one direction forming angles between themselves, being able to have several vectors in the same plane.
- Vectors also have well-defined properties starting with:
- Vectors can be added in two well-defined ways, which entails having the possibility of finding a common result for the entire operation. That is why we have: Vectors can be added by placing vector A first and then vector B so that the end point of the first is connected to the end point of the second vector. This is how the shape of the triangle is formulated.
- Otherwise there is also the possibility of a second form with the union of the vectors, by their starting point forming a diagonal between the two, so that a parallelogram is formed between the two.
- Equality of vectors: when two vectors have the same direction, also carrying the similarity of an equal direction and magnitude, it is said that they have the same characteristics, which is why we are dealing with a concept of equality.
- Vector subtraction: a vector has a negative sign because it retains the same magnitude and direction, but goes in the opposite direction of these and therefore the vector subtraction property is formed.
- Commutative law: if two vectors are added, in any of the two ways presented, no matter what the result is, it will never vary and will always be the same, keeping in mind that A+B = B+A.
- Free vectors: it is the property that indicates that the vectors go from one side to another, parallel to each other.
- Vector multiplication: when two vectors are multiplied, we have that the final result will be a vector with a direction perpendicular to each of the vectors being multiplied, taking this as the product of vectors.
- Unit vectors. It is the one that has a single vector or unit with an equal direction and senses, establishing that it is unique because it meets all the characteristics in a single image or arrow contained in the plane.
- Equivalent vectors: they have the same module with the same meaning in addition to the direction they occupy, but with the difference that the position they have is different for which they receive that name within physics.
- Vectors that have the same direction are those that remain proportional, so they can be kept together within the plane and, furthermore, they are directly proportional in terms of direction, module, and position.
- It is taken into account that in the same plane there can be many vectors that go in the same direction or in a different one, taking into account talking about properties, types and, in addition, counting the characteristics that unite them.
- The vectors also indicate the angles of any element to be delimited in a plane, expressing through mathematical expressions a solution resulting from each of the operations that are carried out.
- A vector in mathematics can be established as a line with sense, module, direction and calculable space also through operations of addition, subtraction and product of lines, so a double concept is handled in the two disciplines.
- It is important to take into account each of the concepts that are handled in terms of the characteristics of the vectors, in order to define if they are vectors that have the same characteristics with each other in the plane.
- Learning to master vectors is like learning multiplication tables, which seems complex, but once you master them, it’s easy.
Tips
- Establish comparisons between each of the vectors that appear in the same plane.
- Being able to do operations with vectors establishes an opportunity to measure a plane.