Vectors. Concepts and sum of vectors

Would you like to learn more about what a vector is and how to operate with vectors?

The online vector simulations on this page will help us to deepen our understanding of this very important mathematical concept that has application in almost all fields of science and technology.

Vectors are fundamental mathematical entities in the fields of geometry and linear algebra. A vector is any mathematical entity that can be represented by an oriented line segment.

Mathematically, a vector is represented by a letter with an arrow on top. Graphically, it is represented by an arrow in n-dimensional space, where each component of the vector represents a quantity in a specific direction. Thus, a vector is defined as a sequence of ordered numbers. For example, a two-dimensional vector can be represented as (x, y), where “x” is the component on the x-axis and “y” is the component on the y-axis. In a three-dimensional space, the vector is represented as (x, y, z), where “z” is the component on the z-axis. Different operations can be performed with vectors, such as addition, subtraction, multiplication by a scalar, scalar product and vector product.

Vectors are widely used in physics, engineering and many other scientific disciplines. They are used to represent physical quantities with direction and modulus, such as forces, velocities and displacements. They are also useful in image processing, artificial intelligence and machine learning, where they are used to represent characteristics or attributes of data. Their study and understanding make it possible to model physical phenomena and solve problems in various fields, which makes them a fundamental tool in the analysis and representation of data and phenomena in the real world.

The online vector simulations on this page will be extremely useful to improve your understanding of this important part of mathematics.

Fundamental concepts of vectors

In this video, about 4 minutes long, the fundamental concepts about vectors and the sum of vectors are reviewed.

Draw a vector

A vector has magnitude and direction. Draw a vector and identify its magnitude and direction.

Components of a vector

A vector can be decomposed into two components perpendicular to each other.

Sum of vectors

Experiment with vector equations and compare vector sums and subtractions. Customize the base vectors or explore scalar multiplication by adjusting the coefficients in the equation. Specify vectors in cartesian or polar coordinates, and view the magnitude, angle, and components of each vector.


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