Given vector a=(1,2), a·b=5,|a-b|=2√5, then |b| equals

|A-b |=2√5
A2-2ab + b2=20 1
A2=|a|2=1 2+2 2=5
Substitute a·b=5, a2=5 into Formula 1
Solve to b2=25,|b|=5

Why the right-hand rule is used to determine the vector cross multiplication direction

This is because the actual results of a large number of experiments to come up with a convenient method of judgment.

This is because the actual results of a large number of experiments to come up with a convenient judge.

What is the difference between point multiplication and cross multiplication of a vector? What is the difference between point multiplication and cross multiplication of vectors?

Distinguish point multiplication from cross multiplication
Point multiplication, also known as the inner product of the vector, the product of quantity.
Vector a. Vector b=|a||b|cos
In physics, the work of force and displacement is actually the inner product of vector F and vector s, that is, the product of points.
Cross multiplication, also known as the outer product of the vector, vector product. As the name implies, the result is a vector, record the vector as c.
|Vector c|=|vector a×vector b|=|a||b|sin
The direction of vector c is perpendicular to the plane where a and b are located, and the direction shall be judged by the "right hand rule "(the direction of vector a is represented by the four fingers of the right hand, then the fingers swing toward the direction of the palm of the hand to the direction of vector b, and the direction of the thumb is the direction of vector c).
Therefore
The outer product of the vector does not follow the multiplicative exchange rate because
Vector a×vector b=-vector b×vector a
In physics, the given moment of force and force arm is the outer product of vector.
The vector is represented by coordinates (three-dimensional vector),
If vector a=(a1, b1, c1), vector b=(a2, b2, c2),
So
Vector a·vector b=a1a2+b1b2+c1c2
Vector a×vector b=
|Ijk|
| A1 b1 c1|
| A2b2c2|
=(B1c2-b2c1, c1a2-a1c2, a1b2-a2b1)
(I, j, k are unit vectors of three coordinate axes perpendicular to each other in space).

What is the difference between point multiplication and cross multiplication of vectors

There are two kinds of multiplication of vectors, called inner product and outer product.
The inner product is also called the quantity product because the result is a number (scalar), and the inner product of vectors a, b is |a||b|cos < a, b
(Where < a, b is the angle between a and b)
The outer product of the vector is also called cross multiplication. The result is a vector, and the direction is perpendicular to the plane |a||b|sin < a, b

There are two kinds of multiplication of vectors, called inner product and outer product.
The inner product is also called the quantity product because the result is a number (scalar) and the inner product of the vectors a, b is |a||b|cos < a, b
(Where < a, b is the angle between a and b)
The outer product of the vector is also called cross multiplication. The result is a vector, and the direction is perpendicular to the plane |a||b|sin < a, b

The difference between dot multiplication and cross multiplication is not in a vector In elementary operations of general real numbers and letters, including unknowns and letters representing known numbers

Vector cross multiplication formula Would you like to know more about vector cross multiplication, about the determinant of the calculation, which book to read? Vector cross multiplication formula Would you like to know more about vector cross multiplication, about determinant calculation, which book should I read?

Given vector a=(1,2), a·b=5,|a-b|=2√5, then |b| equals