If a is collinear with b, then there is a unique real number λ such that b=λa. Why is it wrong? (A, b are vectors)

If a is collinear with b, then there is a unique real number λ such that b=λa. Why is it wrong? (A, b are vectors)

1. The a vector and the b vector are zero vectors.
2. A is zero vector b is not.
3.B is zero vector a is not.λ=0.
We have to consider the possibility of a vector

How to understand that the vector a and b are collinear if and only if there is a unique real number λ such that b=λa

The following assumptions a, b are non-zero.
In analytic terms, the necessary and sufficient condition for a b to be collinear is that their coordinates are proportional, such as a =(3,5), b =(6,10).
You can also imagine a unit vector of length 1 in the direction of a and b, then a, b can be expressed as several times this unit vector, so they can also be multiplied by a constant.
If it is not collinear, it can not be expressed in this way.

For any two vectors a, b, if there is a real number pair (λ, u) which is not all 0, and λa+ub=0, then a and b are collinear.

A+ub=0(vector)
A=-ub
, U is not all 0
Let λ=0
Then a=-u/λ*b
A, b collinear

Why is it wrong that the necessary and sufficient condition of collinearity of plane vectors a, b is the existence of real number x, b (vector)=xa (vector)? Zero vector is not and all directions... Why is it wrong that the necessary and sufficient condition of collinearity of plane vectors a, b is the existence of real number x, b (vector)=xa (vector)? Isn't the zero vector collinear with all vectors? Why is it wrong that the necessary and sufficient condition of collinearity of plane vectors a, b is the existence of real number x, b (vector)=xa (vector)? Zero vector is not and all directions... Why is it wrong that the necessary and sufficient condition of collinearity of plane vectors a, b is the existence of real number x, b (vector)=xa (vector)? Isn't the zero vector collinear with all the vectors?

If a, b are collinear
B=xa when a is a non-zero vector
Because when a is a 0 vector and b is not a 0 vector, there is no real number x such that a=xb
If there is a real number x, b=xa, then there must be a, b collinear, where a need not be a non-zero vector
Because when a is a zero vector, the zero vector is collinear with any vector, then a, b must be collinear

How to find the direction vector after two vectors are multiplied?

The direction vector multiplied by the two vectors is called vector product, and its magnitude is equal to the product of the absolute value of the two vectors and the included angle sine. The direction is determined by the right-hand rule. The specific method is that the right-hand thumb is perpendicular to the remaining four fingers. The direction of the movement of the four fingers represents the direction from the first vector to the second vector. The direction indicated by the thumb is the direction of the vector product. If the vector is represented by coordinates, it can be calculated by determinant.(Note: vector a× vector b=-vector b× vector a)

How to determine the direction of vector multiplication

There is no such thing as multiplication between vectors
Vector has two terms: quantity product and vector product
Both the quantity product and the vector product are operations
Product of quantity: the coordinate corresponding to the vector is multiplied or equal to the product of the module of both and the cosine of the included angle
Vector product: specific number and direction you can see the sixth edition of the first chapter of the second volume of Tongji University, in fact the direction is relatively simple, directly remember, is to meet the right hand rule (specific how to turn you can read the book in detail)
How to say, these are the higher number of relatively basic things, you can take a good look at the higher number