Mathematical definition For mathematical concepts, a vector is a list of numbers, but for programmers, it is more like an array or even a vector in C++ is an array object with variable length. Mathematically distinguish between vectors and scalars.

Mathematically distinguish between vectors and scalars. That is, the corresponding concept in physics, speed is a vector with both magnitude and direction, while speed is a scalar with only magnitude.

The dimension of a vector is the number of numbers contained in the vector. The vector can be any positive dimension. But in computer graphics, two-dimensional, three-dimensional and four-dimensional are commonly used.

In graphics and many programming languages, two-dimensional, three-dimensional and four-dimensional vectors have special conventions. The first is the universal subscript method, which can access all N-dimensional vectors. The other is special. For these three vectors, the four components are represented by x, y, z and w respectively.

Vector can be used to describe both displacement and relative position: the position of an object can be expressed by describing its relationship with a known point. The point used to describe the position is actually a relative position relative to the origin of the coordinate system, so there is the following relationship between the point and the vector.