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Given a, b, c, d are vectors, prove that (a×b)·(c×d)=(a·c)(b·d)-(a·d)(b·c)
(A×b)·(c×d)=(a×b, c, d)=(a×b×c, d)=[(a·c) b-(b·c) a ]·d=(a·c)(b·d)-(a·d)(b·c)
Where (·,·,·) represents the mixed product, and the third equal sign uses the double outer product formula.
Space vector quantity product operation,(a, b)·(c, d)·(e, f), can it be operated The operation of quantity product of space vector,(a, b)·(c, d)·(e, f), can it be operated?
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The vectors a, b, c are known to be orthogonal bases of one unit of space, and the vectors a+b, a-b, c are the other bases of space, if the vector p has coordinates of (1,2,3), Find the coordinates of p under the base a+b, a-b, c,
Let the coordinates of vector p under base a+b, a-b, c be (x, y, z),
Then p=a+2b+3c=x (a+b)+y (a-b)+zc
The result is: a=(x+y) a
2B =(x-y) b
3C=zc
I.e.1= x+y
2=X-y
3= Z
Jiede
X =3/2
Y=-1/2
Z =3
Let the coordinates of vector p be (x, y, z) at bases a+b, a-b, c,
Then p=a+2b+3c=x (a+b)+y (a-b)+zc
The result is: a=(x+y) a
2B =(x-y) b
3C=zc
I.e.1= x+y
2=X-y
3= Z
Solved
X =3/2
Y=-1/2
Z =3
Let the vector p be (x, y, z) at the coordinates of bases a+b, a-b, c,
Then p=a+2b+3c=x (a+b)+y (a-b)+zc
The result is: a=(x+y) a
2B =(x-y) b
3C=zc
I.e.1= x+y
2=X-y
3= Z
Jiede
X =3/2
Y=-1/2
Z =3
What is the condition for a 3-point collinear space vector? What is the condition that three points P1(x1, y1, z1), P2(x2, y2, z2), P3(x3, y3, z3) are in a straight line? Please explain in detail ~ Thank you
(Z2-Z1)/(Z3-Z2)=(Y2-Y1)/(Y3-Y2)=(X2-X1)/(Y3-Y2)
How to Decompose a Rank 1 Matrix into Column Vector and Row Vector by Matlab Language
The upstairs method is obviously flawed, for example for A =[0 0; 0 1].
Can be done with SVD,[ u, s, v ]= svds (A,1), then A=u*s*v'
After finding the rank of the matrix, how to obtain a maximal independent group of the travel vector group? 3 1 0 2 1 -1 2 -1 1 -1 2-1 Reduced row ladder matrix 0 4 -6 5 1 3 -4 4 0 0 0 0 Rank =2 How to the rank of the matrix, how to obtain a maximal independent group of the travel vector group? 3 1 0 2 1 -1 2 -1 1 -1 2-1 Reduced row ladder matrix 0 4 -6 5 1 3 -4 4 0 0 0 0 Rank =2 How to the rank of the matrix, how to obtain a maximal independent group of the travel vector group? 3 1 0 2 1 -1 2 -1 1 -1 2-1 Reduced row-order ladder matrix 0 4 -6 5 1 3 -4 4 0 0 0 0 Rank =2
Well, just take a look with the naked eye.
For example, the rank of your matrix is 2.
Then you find a full - rank 2 X 2 small matrix.
The row vector group must be a maximal independent group.
In fact, you can already find 2X2 small matrix in the process of seeking rank, otherwise how do you know its rank is 2
Well, just take a look at it with the naked eye.
For example, the rank of your matrix is 2.
Then you find a full-rank 2X2 small matrix.
The row vector group must be a maximal independent group.
In fact, you can already find 2X2 small matrix in the process of seeking rank, otherwise how do you know its rank is 2
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