Vector base refers to two non-zero vectors e 1 and e2, which can represent any vector a in plane geometry. Expressed as a=xe 1+ye2, when vector a is expressed by bases e 1 and e2, the values of real numbers x and y are unique.

Vector base should pay attention to the following points:

Significance of mathematical vector basis: In plane geometry, two non-zero nonlinear vectors e 1 and e2 of arbitrary vector A can be represented.

On the plane, any vector A (including zero vector) can be represented by two non-zero vectors (e 1, e2) of non-* * lines, that is, a=xe 1+ye2(x, y is any real number). This is the main content of the basic theorem of plane vector. The two nonzero vectors e 1 and e2 used to represent vector a here are called a set of bases of vector a. ..

Mathematical vector:

One of the most basic concepts in mathematics. It is a mathematical abstraction of speed, acceleration, force and other quantities with magnitude and direction. Usually, an arrow is added to Latin letters or black italic letters are used to represent vectors, and two operations, such as addition and number multiplication, are defined in vectors. Compared with vectors, quantities that only represent size are often called quantities, also called scalars or scalars.

Modern times adopt the axiomatic definition of vector, and think that vector is an element of vector space or linear space. In analytic geometry, geometric line segments (that is, ordered point pairs) in public space intuitively represent vectors, sometimes called geometric vectors.

1. The vector as the base cannot be a zero vector, that is, e 1≠0 and e2≠0 (where 0 refers to a zero vector), and e 1 and e2 are not * * * lines (parallel);

2. A set of bases is not a nonzero vector, but refers to two nonzero vectors;

3. When vector A is represented by cardinality e 1 and e2, the values of real numbers x and y are unique. When the cardinality is e 1 and e2, there is only one pair of real numbers (x, y) such that a = xe1+ye2;

4. It can be said that the basis of vector A is not unique. Substrates e 1 and e2 can express vector a as a=xe 1+ye2, and another group of substrates f 1 and f2 can also express vector a as a=mf 1+nf2.