It can be imagined as a line segment with an arrow. The arrow indicates the direction of the vector; Line segment length: indicates the size of the vector. Only the magnitude corresponds to the vector, and the quantity without direction is called quantity (called scalar in physics).
Vector notation: print letters (such as A, B, U, V) in bold, and add a small arrow "→" at the top of the letter when writing.
If the starting point (a) and the ending point (b) of the vector are given, the vector can be recorded as AB (plus sign →) at the top. In the spatial cartesian coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the Oxy plane is a vector.
In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction.
Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.
Vectors were originally applied to physics. Many physical quantities such as force, velocity, displacement, electric field intensity measurement and magnetic induction intensity are vectors.
Around 350 BC, Aristotle, a famous ancient Greek scholar, knew that force can be expressed as a vector, and the resultant force of two forces can be obtained through the famous parallelogram rule.
The word "vector" comes from directed line segments in mechanics and analytic geometry. Newton, a great British scientist, was the first to use directed line segments to represent vectors.
Vector can enter mathematics and develop, first of all, we should start with the geometric representation of complex numbers. At the end of18th century, wiesel, a Norwegian surveyor, first expressed the complex number A+Bi with points on the coordinate plane (A and B are both rational numbers, and they are not equal to 0 at the same time), and defined the vector operation with geometric complex operation.
Points on the coordinate plane are represented by vectors, and the geometric representation of vectors is used to study geometric problems and trigonometric problems.
People gradually accepted the complex number and learned to use it to represent and study the vector on the plane, so the vector quietly entered mathematics.