Concrete examples of the application of vectors in daily life and scientific research, about 300 words?

Vectors can be seen everywhere in daily life, and they should become the basic common sense of mathematics that future citizens should understand. For example, the weather forecast mentions "wind force level 3, wind direction northeast", which includes two factors: magnitude and direction. As for the position vector, it involves two parts: "distance" and "direction". The sum of the thrust of the water flow in the river and the power of the ship is a vector picture representation that I have been exposed to in elementary school. In mathematics, points are usually used to represent positions and rays are used to represent directions. In a plane, all rays starting from any point can be represented by To represent various directions in the plane. The representation of a vector is often represented by a directed line segment. The length of the directed line segment represents the size of the vector, and the direction pointed by the arrow represents the direction of the vector. Vectors can also be represented by the letters a and b. , c, etc., or represented by the starting point and end point letters of the directed line segment representing the vector. The size of the vector, that is, the length (or module) of the vector, is denoted by |a| A vector with a length of 0 is called a zero vector, denoted by Make 0. A vector whose length is equal to 1 unit length is called a unit vector.

Vectors are also called vectors and were originally used in physics. Many physical quantities such as force, speed, displacement, electric field intensity, magnetic induction intensity, etc. are vector. About 350 BC, the famous ancient Greek scholar Aristotle knew that force can be expressed as a vector, and the combined effect of two forces can be obtained by the famous parallelogram rule. The word "vector" comes from mechanics and analytical geometry. Directed line segments in . The British scientist Newton was the first to use directed line segments to represent vectors. Surveys have shown that the vectors used in general daily life are quantities with geometric properties. Except for zero vectors, arrows can always be drawn to represent directions. But there are more extensive vectors in advanced mathematics. For example, consider all real coefficient polynomials as a polynomial space, and the polynomials here can be regarded as a vector. In this case, it is necessary to find the starting point and end point or even It is impossible to draw an arrow to indicate the direction. The vectors in this space are much broader than the vectors in geometry and can be any mathematical or physical object. In this way, we can guide the application of linear algebra methods in the vast field of natural science. Therefore, the concept of vector space has become the most basic concept in mathematics and the central content of linear algebra. Its theory and methods have been widely used in natural science. It has been widely used in various fields. Vectors and their linear operations also provide a concrete model for the abstract concept of "vector space".

From the perspective of the history of mathematics development, for a long time in history, the vector structure of space was not recognized by mathematicians. It was not until the end of the 19th century and the beginning of the 20th century that people combined the properties of space with vector operations. Connected together, vectors become a mathematical system with excellent operational properties. The stage when vectors entered mathematics and developed was at the end of the 18th century. The Norwegian surveyor Wiesel first used points on the coordinate plane to represent complex numbers a+bi, And use complex number operations with geometric meaning to define vector operations. Represent points on the coordinate plane as vectors, and use the geometric representation of vectors to study geometric and trigonometric problems. People gradually accepted complex numbers, and also learned to use complex numbers to represent and study vectors in the plane. In this way, vectors entered mathematics quietly.

However, the use of complex numbers is limited, because it can only be used to represent a plane. If there are forces that are not on the same plane acting on the same object, you need to find the so-called three-dimensional "complex numbers" and the corresponding operations. System. In the mid-19th century, the British mathematician Hamilton invented quaternions (including the quantity part and the vector part) to represent vectors in space. His work laid the foundation for the establishment of vector algebra and vector analysis. Subsequently, the electromagnetic theory The discoverer, the British mathematical physicist Maxwell, separated the quantity part and the vector part of quaternions, thus creating a large number of vector analyses.

The creation of three-dimensional vector analysis, and the same four-dimensional vector analysis The formal split of ternions was independently completed by Gubers and Heaviside in the UK in the 1880s. They proposed that a vector is just the vector part of a quaternion, but is not independent of any quaternion. They introduced two types of multiplication, namely quantity products and vector products. They also extended vector algebra to vector calculus of variable vectors. Since then, the vector method has been introduced into analysis and analytic geometry, and gradually improved, becoming An excellent set of mathematical tools.,5,