Vectors – Definition & Properties


You must have heard of the mathematical term – Vectors. Vectors are two-dimensional geometrical entities with magnitude and direction. It is shown by a straight line with an arrow pointing in the direction of the vector, and the length of the vector shows the magnitude of the vector. As a result, vectors are shown by arrows having initial and terminal points. Over the course of 200 years, the concept of vectors evolved. Many of the physical quantities are represented by vectors such as displacement.

Furthermore, after the introduction of electromagnetic induction in the late nineteenth century, the use of vectors began. You can always visit Cuemath Website to learn the topic for clarity in the chapter in an awesome way.

Vectors in Euclidean Geometry

Vector is an important mathematical topic and is a geometric figure having magnitude and direction. They have an initial point called the starting point and the final or termination point which is the ending of a vector. Vectors can be divided, multiplied, subtracted as well as added too.

In this article, we will look at vector operations in-depth and learn about them.

Operations on Vectors

Some basic vector operations can be performed geometrically without the use of a coordinate system. These vector operations are represented by a scalar’s addition, subtraction, and multiplication. In addition, there are two methods for multiplying two vectors together: the dot product and the cross product. These are briefly explained further down. You can read more about all these vector operations with examples on Cuemath. Learning these topics will give clarity on vectors and their operations.

  • Addition of Vectors – How to add two vectors
  • Subtraction of Vectors – How to subtract two vectors
  • Scalar Multiplication – How to multiply the given vectors
  • Scalar Triple Product of Vectors – How to find the scalar triple product of vectors

Applications of Vectors

Vector algebra is used to measure angles and distances between panels in satellites, in the construction of pipe networks in various industries, and in calculating angles and distances between beams and structures in civil engineering.

Vectors are used in a variety of real-world situations, including those involving force or velocity. Consider the forces at work on a boat crossing a river. The boat’s motor creates a force in one direction, while the river current creates a force in the opposite direction. Both of these forces are vectors.

Definition of Coordinate Plane

A two-dimensional surface formed by two number lines is known as a coordinate plane. The x-axis refers to a horizontal number line. The other number line is the vertical number line, which is referred to as the y-axis. These two axes x and y intersect at a point which is known as the origin.

Quadrants on a Coordinate Plane

A quadrant is a region/part of a cartesian or coordinate plane obtained when the two axes intersect each other. There are a total of 4 quadrants on the coordinate plane.

Vectors Belong to What Branch of Mathematics?

Linear algebra is concerned with vector spaces, which are distinguished by their dimension, which roughly corresponds to the number of independent directions in the space. Infinite-dimensional vector spaces naturally arise in mathematical analysis as function spaces with vectors that are functions.

What Is the Difference Between Scalars and Vectors?

The only distinction between scalars and vectors is that a scalar is a quantity that is independent of direction, whereas a vector is a physical quantity that has both magnitude and direction. Scalars are commonly used to describe distance, speed, and time. These are actual values accompanied by their measurement units. Vectors are commonly used to indicate the direction and magnitude of quantities such as displacement, velocity, acceleration, and force.

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