Given a non-zero vector, ab is a parallel to b is a necessary fly sufficient equal to b why?

A = b It is certainly possible to deduce that a and b are in the same direction, i.e. parallel; but a and b are parallel, but not necessarily equal in length, and a = b can not be deduced. Therefore, a and b are necessary and insufficient conditions for a = b to be parallel

A = b It is certainly possible to deduce that a and b are in the same direction, i.e. parallel; but a and b are parallel, but the length is not necessarily equal and a = b can not be deduced. Therefore, a and b are necessary and insufficient conditions for a = b to be parallel

The module of vector a is equal to the module of vector b and is not equal to 0, and a, b are not collinear. What is the relationship between a+b and a-b? Important analysis. The following should be vector a+b, vector a-b

(A+b)*(a-b)=a*a-a*b+b*a-b*b
=|^2-|^2
=0
Therefore: a+b is perpendicular to a-b

It is known that a, b are non-zero vectors, and the module of a = the module of b = the module of a-b, find the angle between a and a+b (Vector symbol omitted) It is best to write the complete process in a complete formula It is known that a, b are all non-zero vectors, and the module of a = the module of b = the module of a-b, find the angle between a and a+b (Vector symbol omitted) It is best to write the complete process in a complete formula It is known that a, b are non-zero vectors, and the module of a = the module of b = the module of a-b, find the angle between a and a+b (Vector symbol omitted) It would be better to write the complete process in a complete formula

As shown in the figure,

Let AB=a, AD=b

Then DB=a-b

Module of a=module of b=module of a-b

Parallelogram ABCD is diamond

AC=a+b

The angle between AC and AB is 30°,

I.e. the angle between a and a+b is 30°

Given that the nonzero vectors a, b satisfy the modulus of a-b = the modulus of a+b = the modulus of b (λ>=2), then the maximum value of the angle between the vectors a-b and a+b is? If the non-zero vector a, b satisfies the module of a-b = the module of a+b = the module of b (λ>=2), then the maximum value of the angle between vector a-b and a+b is?

Module of a-b=module of a+b
∴(A-b)2=(a+b)2
4A.b=0
A b
Module of a+b=module of b
∴(A+b)2=( b)2
A2+b2+2a.b=λ2b2
A2=(λ2-1)|b|2
(A+b)·(a-b)=|a|2-|b|2=(λ2-2)|b|2
|A-b|2=|a+b|2=|a|2 b|2=λ2|b|2
Cos
=(A+b)·(a-b)/(|a+b a-b|)
=(λ2-2)|B |²/(λ2|b|2)
=(λ²-2)/λ²
=1-2/λ²
∵ λ≥2,
∴ λ²≥4,
∴ -1/λ²∈[-1/4,0)
∴ 1-2/λ²∈[1/2,1)
I.e. at maximum angle, the cosine is 1/2
The angle is 60°.

If a number is subtracted from itself, and their sum-difference quotient adds up to 18.8, the number is () Five minutes! Come on! Thank you all! ~ The best answer is who plays the process first, not the equation A number is subtracted from itself, and their sum-difference quotient adds up to 18.8 which is () Five minutes! Come on! Thank you all! ~ The best answer is who plays the process first, not the equation

What is the sum, difference, and quotient of the sum, difference, and division of an uncle that adds, subtracts, and divides himself What is the sum, difference, and quotient of the sum, difference, and division of an uncle who adds, subtracts, and divides himself

Given a non-zero vector, ab is a parallel to b is a necessary fly sufficient equal to b why?