Cross Product and Vector Multiplication

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Melissa
Melissa il 19 Ago 2013
Commentato: Nitin Phadkule il 17 Set 2021
If i have the following 4 vectors:
D=Ax(B*C)
How would I solve for C?
Try and make this a tab bit more clear. I have A is a 1x3 matrix, B is a 3x3 matrix C is a 3x1 matrix and D is a 1x3 matrix. I am trying to solve for C. The problem is stated as A cross the product B*C equals D.
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Melissa
Melissa il 19 Ago 2013
Its a stiffness and force equation for displacement. So D is reaction force of [Fx,Fy,Fz]. A is the position vector [x;y;d]. B is the transformation to global stiffness [3x3 DCM] and C is the displacement [x.y.z]
Melissa
Melissa il 19 Ago 2013
>> A=[1 2 3]; B=[1 2 3; 4 5 6; 7 8 9]; C=[4; 5; 6];
>> D=cross(A,B*C)
D =
13 -26 13

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Roger Stafford
Roger Stafford il 19 Ago 2013
C = [ cross(A',B(:,1)) , cross(A',B(:,2)) , cross(A',B(:,3)) ]\(D');
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Melissa
Melissa il 19 Ago 2013
That makes sense. I went through the properties of cross product and multiplication and arrived at your equation but since it is singular then I cannot obtain C. Dang. Thank you for your time and explanation.
Roger Stafford
Roger Stafford il 19 Ago 2013
There is a way to obtain a unique value for C that satisfies your equation. Let C be given by:
C = B\(cross(D',A')/dot(A,A));
This is the unique C such that
D' = cross(A',B*C)
and
dot(B*C,A') = 0
That is, such that B*C is orthogonal to A'. It assumes that D is orthogonal to A and that B is non-singular.

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Più risposte (3)

joseph agno
joseph agno il 7 Ott 2020
  • Find the Matlab command to carry out the cross product of two vectors b and c and try it out on two vectors.
muhammad asif
muhammad asif il 11 Ott 2020
if n corss n = ny
how to write cross in symbol notation form in matlab
muhammad asif
muhammad asif il 11 Ott 2020
circle statement
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Steven Lord
Steven Lord il 11 Ott 2020
Do you mean n times n? If so use the * operator.
But please do not put your own files in any subdirectory under the matlabroot directory!

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