If e1 and e2 are a set of substrates in the plane, the following four sets of vectors can be used as the substrates of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2 If e1, e2 are a set of bases in the plane, the following four sets of vectors can be used as the bases of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2

If e1 and e2 are a set of substrates in the plane, the following four sets of vectors can be used as the substrates of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2 If e1, e2 are a set of bases in the plane, the following four sets of vectors can be used as the bases of the plane vector: A, e1-e2, e2-e1B,2e1-e2, e1-1/2e2C,2e2-3e1,6e1-4e2D, e1+e2, e1-e2

Select D.
Since e1, e2 are a set of substrates in the plane, e1, e2 are not collinear
Therefore, e1+e2, e1-e2 are not collinear, i.e. can be used as the base of plane vector.

In the following vector group, e1=[0,0] e2=[1,-2] e1=[-1,2] e2=[5,7] Ce1=[3,5] e2=[6,10] de1=[2,-3] e2=[1/2,-3/4]

Two non-collinear vectors can be used as all vector bases in the plane.
E1=(-1,2), e2=(5,7),-1×7-2×5=-17=0, so it is not collinear.

Let vector e1, vector e2 be a set of substrate on a plane, Let vector AB=vector e1+vector e2, vector BC=2vector e1+8vector e2, vector CD=3(vector e1-vector e2), (1) Alignment: A, B and D are collinear; (3) If vector AB=2 vector e1+k vector e2, vector CB=vector e1+3 vector e2, vector CD=2 vector e1-vector e2, find the k value of vector A, B, D collinear

AB=e1+e2, BC=2e1+8e2, CD=3(e1-e2)
(1)
BD=CD+CD=5e1+5e2=5(e1+e2)=5AB
=> AB//BD
=> A,B,D 3 point collinear
(3)
AB=2e1+ke2, CB=e1+3e2, CD=2e1-e2
BD = BC + CD = e1-4e2
A, B, D collinear
=> AB = mBD
2E1+ke2=m (e1-4e2)
=>2= M and k =-4 m
=> K=-8

Is it right to judge the following statement about vectors? 1. A collinear vector is a vector that can be moved to the same line 2. A parallel vector is a line in which the vector is parallel 3

1 Correct
2 Error
The vector has only two elements:1 direction 2 size, no position difference.

If e1 and e2 are two non-collinear vectors in the plane α, then ()1λe1 e2(λ, R), which is wrong in the following statements, can represent all the vectors in the plane α; 2 For any vector a in the plane α, if a=λe1 e2, there are many pairs of μ; 3 If the vector λ1e1 1e2 is collinear with λ2e1 2e2, then there is only one real number k, so that λ2e1 2e2=k (λ1e1 1e2); 4 If the real number λ,μ is such that λe1 e2=0, then λ=μ=0. A.12 B.23 C.34 D.2 only

D
2: Take a=e1 or e2, each with only one case

About the vector, which of the following two statements is correct 1 If the module of vector a=the module of vector b, then vector a=vector b, or vector a=negative vector b 2 If vector a=vector b, vector b=vector c, then vector a=vector c Which of the above two statements is correct and which is wrong? What is the reason for the mistake? How to correct it?

The modules of the first error vector are identical, and the directions can be completely arbitrary. For example, the modules of the vector (1,1) are the root number 2, and the modules of the vector (1,1-1) are the root number 2, but they are neither equal nor opposite. If the two vectors are parallel, then the vector a = the vector b, or the vector a = the negative vector b
The second one.