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Given that (a cross multiplication b) point multiplication c equals 2, find [(a+b) cross multiplication (a-b)] point multiplication c
(AXb).c=2
(A+b) X (a-b)].c=2
How to calculate the cross multiplication between two vectors such as A (a, b, c) B (d, e, f)? It would be best to give the derivation, and the principle How to calculate the cross multiplication between two vectors such as A (a, b, c) B (d, e, f)? It would be best to give the derivation and the principle
Speaking of cross multiplication of two vectors, the vector must be a space vector
Let vector AB = vector a - vector b, vector CD = vector a + vector b
Vector AB=(x1, y1, z1), Vector CD=(x2, y2, z2)
Vector AB×vector CD=(y1z2-z1y2, x2z1-x1z2, x1y2-y1x2)
A new vector is generated whose direction is perpendicular to the plane defined by vector AB, vector CD and whose direction is defined by the right-hand rule.
Multiplication of points: work, force-direction product, etc.
The result of cross multiplication is a vector, perpendicular to the original two planes, the direction is also determined by the original two vectors.
In short, the result of dot multiplication is the number
The result of cross multiplication is still a vector
The Problem of Matrix and Vector Cross Multiplication M represents a 3*3 matrix, a, b represents a 3*1 vector respectively. Now that the values of M*a and M*b are known (but the exact values of M, a, b are unknown), how to solve the value of M*cross (a, b)? Where cross (a, b) represents the cross multiplication of a and b. The Problem of Matrix and Vector Cross Multiplication M represents a 3*3 matrix, a, b represents a 3*1 vector respectively. Now that the values of M*a and M*b are known (but the exact values of M, a, b are unknown), how to solve the value of M*cross (a, b)? Where cross (a, b) is the cross multiplication of a and b.
It's usually unsolved. For example:
Take M as the identity matrix of 3*3, a=(1,0,0), b=(0,1,0)(I will not transpose, it must be a column vector anyway), then M*a=a, M*b=b, where M*cross (a, b)=cross (a, b). Then take N as the following matrix:
1 0 0
0 1 0
0 0 2
It is easy to find N*a=a, N*b=b, but N*cross (a, b)=2cross (a, b). Therefore, given the same M*a, M*b, different M*cross (a, b) will appear.
(Point A times B) C is not equal to C (point B times A)? Is C and the whole in parentheses also dot-multiplied? And what is a cross multiplication (BC)? Here... (Point A times B) C is not equal to C (point B times A)? Is C and the whole in parentheses also dot-multiplied? And what is a cross multiplication (BC)? Is dot multiplication omitted between B and C? (Point A times B) C is not equal to C (point B times A)? Is C and the whole in brackets a dot-multiply relationship? And what is BC equal to? Here... (Point A times B) C is not equal to C (point B times A)? Is C and the whole in brackets a dot-multiply relationship? And what is BC equal to? Is dot multiplication omitted between B and C?
A point multiplied by B is the same as B point multiplied by A, so (A point multiplied by B) C is equal to C (B point multiplied by A)
But the multiplication of vector and number is not point multiplication or cross multiplication
The dot multiplication between B and C is not omitted because the result of dot multiplication between B and C is a number.
A point multiplied by B is the same as B point multiplied by A, so (A point multiplied by B) C is equal to C (B point multiplied by A)
And the multiplication of vector and number is not point multiplication or cross multiplication
There's no point multiplication between B and C because the result of point multiplication between B and C is a number.
Given the vector a-b=(5,2-in), b=(1,-2), if a is parallel to b, then in =
Given the vector a-b=(5,2-in), b=(1,-2),
Because a//b
So
A-b//b
I.e.
5/1=(2-In)/(-2)
2-In=-10
Enter =12
Given the vector a-b=(5,2-in), b=(1,-2),
Because a//b
So
A-b//b
I.e.
5/1=(2-In)/(-2)
2-In=-10
In =12
Given the vector a=(1,2) b=(x,1), and a+b is parallel to a-b, then x
A + b =(1+x,3)
A-b=(1-x,1)
A+b is parallel to a-b, then a+b=λ(a-b)
I.e.1+x=λ(1-x),3=λ*1
Then λ=3, x=1/2
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