Unitary vector definition - What it is, Meaning and Concept
The vectors are, in the field of physics , magnitudes defined by their point of application, their meaning, their direction and their value.According to the context in which they appear and their characteristics, they are classified differently.
The idea of unit vector refers to the vector whose module is equal to 1 .It should be remembered that the module is the figure that coincides with the length when the vector is represented in a graph.The module is thus a norm of the mathematics that is applied to the vector that appears in a Euclidean space.
Another of the names by which the unit vector is known is normalized vector , and it appears very frequently in problems of various fields, from mathematics to computer programming.It is possible to obtain the internal product or scalar product of two unit vectors by finding out the cosine of the angle that forms between them.The product of a unit vector by a unit vector In this way, it is the scalar projection of one of the vectors on the direction established by the other vector.
When you have a vector and you want to normalize it, what you do is look for a unit vector that Have the same meaning and the same direction as the vector in question.The normalization of the vector is carried out by dividing the vector by its module.The result is a unit vector with identical direction and identical direction.
But what does it mean to divide the vector by its module? Let's not forget that the vector is defined by means of components, as many as dimensions are in the space in which it is located.If we take a two-dimensional vector, expressed in the X axes and Y , then it will have a value for each of them, such as (4,3).It should be mentioned that these components are also known by the name of vector terms .
Therefore, if we go back to the method to find the unit vector that consists of dividing the original by its module, simply we must take each of the components and divide them by that value , so that the final result offers us a module equal to 1.This may seem too abstract or arbitrary for people outside of mathematics, but once analyzed carefully it is absolutely logical.Let's see the explanation below.
If we rely on the rules of the division for a moment, we will remember that every number is divisible by itself and by 1 , and that if we divide it by itself the result we get is precisely 1.Now, in this case we are looking for a vector whose components orient it in the same direction of the original, but that generate a different length, more specifically, of value 1.
Going back to the procedure of dividing each component by the module, let's see how to get to that step in a logical way.First, it is necessary to remember that to calculate the module of a vector we rely on the Pythagorean theorem , since we consider the vector segment as the hypotenuse, and each of its components as the legs of the triangle.
Therefore, to calculate the module of the vector (4,3) we must obtain the square root of the sum of the squares of 4 and 3.This results in 5.To arrive at the unit vector, we must multiply all for 1/5 (a fifth), so that on one side of equality we get 1 (the length of the normalized vector) and on the other we find 1/5 x (4 , 3) .
Finally, we can say that the components of the unit vector will be (4/5,3/5), and just apply the Pythagorean Theorem to verify that the module is indeed 1.
The use of unit vectors facilitates the specification of the different directions that the vector quantities present in a given coordinate system.
The idea of unit vector refers to the vector whose module is equal to 1 .It should be remembered that the module is the figure that coincides with the length when the vector is represented in a graph.The module is thus a norm of the mathematics that is applied to the vector that appears in a Euclidean space.
Another of the names by which the unit vector is known is normalized vector , and it appears very frequently in problems of various fields, from mathematics to computer programming.It is possible to obtain the internal product or scalar product of two unit vectors by finding out the cosine of the angle that forms between them.The product of a unit vector by a unit vector In this way, it is the scalar projection of one of the vectors on the direction established by the other vector.
When you have a vector and you want to normalize it, what you do is look for a unit vector that Have the same meaning and the same direction as the vector in question.The normalization of the vector is carried out by dividing the vector by its module.The result is a unit vector with identical direction and identical direction.
But what does it mean to divide the vector by its module? Let's not forget that the vector is defined by means of components, as many as dimensions are in the space in which it is located.If we take a two-dimensional vector, expressed in the X axes and Y , then it will have a value for each of them, such as (4,3).It should be mentioned that these components are also known by the name of vector terms .
Therefore, if we go back to the method to find the unit vector that consists of dividing the original by its module, simply we must take each of the components and divide them by that value , so that the final result offers us a module equal to 1.This may seem too abstract or arbitrary for people outside of mathematics, but once analyzed carefully it is absolutely logical.Let's see the explanation below.
If we rely on the rules of the division for a moment, we will remember that every number is divisible by itself and by 1 , and that if we divide it by itself the result we get is precisely 1.Now, in this case we are looking for a vector whose components orient it in the same direction of the original, but that generate a different length, more specifically, of value 1.
Going back to the procedure of dividing each component by the module, let's see how to get to that step in a logical way.First, it is necessary to remember that to calculate the module of a vector we rely on the Pythagorean theorem , since we consider the vector segment as the hypotenuse, and each of its components as the legs of the triangle.
Therefore, to calculate the module of the vector (4,3) we must obtain the square root of the sum of the squares of 4 and 3.This results in 5.To arrive at the unit vector, we must multiply all for 1/5 (a fifth), so that on one side of equality we get 1 (the length of the normalized vector) and on the other we find 1/5 x (4 , 3) .
Finally, we can say that the components of the unit vector will be (4/5,3/5), and just apply the Pythagorean Theorem to verify that the module is indeed 1.
The use of unit vectors facilitates the specification of the different directions that the vector quantities present in a given coordinate system.
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