When studying mathematics at high school, students have to deal with a topic concerning the magnitude of a vector. The term magnitude is commonly used not only in mathematics, but also in physics and is an integral part of the overall course of the high school education program. In terms of mathematics, the magnitude describes the size of particular mathematical object. This is a kind of property which is used when it comes to comparing that or another object with other objects and identify whether it is bigger or smaller than other objects, which are also of the similar type. In other words, the magnitude is used when one needs to rank the category of particular objects to which the given object (the one that is being compared) belongs. Many assignments on mathematics ask students to find the magnitude of a vector. Dealing with these assignments has a lot of methods, which depends on the data provided in the assignment and on the complexity level of the assignment. In this article, you will get familiar with the common ways to find the magnitude and learn some essentials which will help you understand this aspect of mathematics better.
A good starting point before you learn what is the magnitude would be figuring out the meaning and the common definition of the term «vector». The word «vector» may refer to various meanings, used in different aspects of mathematics, including geometry, and physics. Generally speaking, without referring to any specific area of science, a vector is considered to be a component of a vector space. When talking of a vector space, which is sometimes is also called a linear space, one should mean a number (a set) of certain objects of the same class. These objects are called vectors. They can be scaled (multiplied) by different numbers and also they can be added one to another. The numbers that the vectors can be multiplied by are called scalars, and are characterized by all kinds of real numbers that can be calculated by means of one real number. In case if you don't know in terms of what area of mathematics you are dealing with that or another vector, the provided above definition is acceptable to apply.
When it comes to geometry, linear algebra as a branch of mathematics, and physics, the definition of a vector may be a little different. First of all, the vector used in geometry is called a Euclidean vector. Second of all, its properties and characteristics are also different. This kind of vector is used to describe physical quantities, both of which are considered to have a particular direction and magnitude. Euclidean vectors represent a vivid example of a vector space that was mentioned earlier in the article. This kind of vectors are expressed in so-called forces, which are specific physical quantities. Within the vector space, you can take two elements (forces) of the same type and add them one to another and add them to yield a third. Having said that, it is not necessarily that the elements of the vector space are visual objects in the form of arrows, although this is how they usually are represented. On the contrary, they can be abstract; elements of the vector space can be mathematical objects with certain characteristics and properties, which can be expressed in the form of arrows, but at the same time remain abstract.
The magnitude of a vector serves to represent the size of the objects the explanation of which is provided above. It helps compare various elements of the same class but with different characteristics between each other and find out which one is larger or smaller, etc.
Depending on the discipline where the term magnitude of a vector is used, it has different purposes and characterized differently. In terms of linear algebra, vector spaces are characterized in a different manner from how they are characterized in terms of geometry, for example. Their common and the main characteristic, when it comes to linear algebra, is the dimension. As a matter of fact, this characteristic is usually used in order to specify the particular number of separate directions located within the vector space that are independent one from another. Also, there may be extra structures within the vector space, which are expressed in the form of a so-called inner product or norm product. As a rule, spaces like these occur in such branch of mathematics as mathematical analysis, which is dedicated to the study of continuos changes and contains a number of different theories, including but not limited to analytic functions, integration, infinite series and others. Analytical problems occurring within the study of mathematical analysis require capability of identifying various phenomena, like whether a set of given elements of the vector space converges to a particular element.
If to discuss the vector space through the prism of history, it has to be mentioned that the first discussions concerning the subject of vector spaces took place in the seventeenth century. At that times, this issue has been researched within various aspects of mathematics, including analytic geometry, Euclidean vectors, matrices, the theory of systems and linear equations (the subject of study of linear algebra) and so on. In contemporary world, there is also a wide range of areas where the usage of vector spaces is a common occurrence. Among such areas, are not only mathematics and physics, but also science, engineering. In addition, since the beginning of computer era, vector spaces have been used in computer science also.
Now that you are aware of essentials concerning vectors as a subject of study of mathematics and particularly geometry, you can proceed to learning how to deal with finding of the magnitude of a vector. Such parameter as vector is often faced in a wide range of geometry and physics problems. As a matter of fact, students find such assignments quite difficult to accomplish, because they require not only lots of theoretical knowledge, but also ability to think in an analytical manner. As for the magnitude, it can be explained as the length of the given vector. At the same time, the direction is considered to be the point at which the vector is directed. The methodology of measuring the magnitude of a vector consists of a number of steps that are described below. Read them attentively and follow when completing your assignment.
The method provided above is good to use when you need to find the magnitude at the origin. On the other hand, however, there are other methods, depending on the information and requirements provided in the assignment. For example, if you need to find the magnitude from the origin, you will have to undertake the following steps. Read them carefully.
These are the guidelines that will help you deal with your assignment requiring to find the magnitude. Following them will make it easier for you to deal with it. At the same time, remember about the opportunity to use professional assistance. Apart from help with mathematics, you can also get the following kinds of writing services: