Unlike scalar quantities, which have only one component, vector quantities consist of two components. Some common examples of scalars are time, speed, energy, mass, volume, area, and height.Ī vector quantity has both magnitude and direction. Scalars are represented by simple letters like a or A, and they typically consist of real numbers. Though they are related, vectors and scalars are used in different situations.Ī scalar quantity has magnitude but no direction. Physical and mathematical quantities are classified as either vectors or scalars. Vectors are often represented by boldface letters like a or A. If boldface is not possible, such as when writing notes by hand, a vector is represented by a letter with an arrowhead above it. This means that the vector is displaced from the origin by two points along the horizontal (x-axis) and four points along the vertical axis (y-axis). In the image below, the vector OA is represented as a column vector. This representation is called a column vector. The direction of the vector is basically the same as the direction of the arrow.Īlgebraically, a vector can be expressed as an ordered pair. The magnitude of the vector is basically the same as the length of the line segment ab. Although this example shows a vector in two dimensions, it can also have three, four, or higher dimensions. Point a is called the initial, or starting, point, and point b is called the terminal or ending point of the vector A. |A| represents its length (or magnitude), and the arrowhead pointing from point a to point b represents its direction. The image below is an example of a geometric representation of a vector.Ĭonsider the following figure where A is a vector. The vector’s length represents its magnitude, whereas the direction indicates its direction concerning a set of coordinates. Vectors can be geometrically represented by straight arrows of a specific length pointing in a specific direction with specific starting and ending points. Geometric and Mathematical Representation of Vectors
Geometric and Mathematical Representations of Vectors.In this section, we will learn about the following important vector concepts: Since vectors express two notions, namely magnitude, and direction, they can construct a wide variety of mathematical models for various problems and scenarios. However, as time has passed, vectors have become widely used in many fields, including linear algebra, engineering, computer science, structural analysis, and navigation. Historically, vectors were used in geometry, physics, and mechanics. Using the above definition, we can see that the representation of vectors requires the presence of two components, namely: “An object or the physical quantity which can be represented by both magnitude and direction.” In physics and mathematics, a vector is defined as: Have you ever wondered what makes speed different from velocity or mass different from weight? Hint: The answer is related to vectors! We will explore these questions and more as we discuss the following vector topics in this article: Vectors are mathematical quantities used to represent objects that have both magnitude and direction.
Vectors efficiently convey information about a mathematical or physical element. What is a Vector? – Explanation & Examples
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