Cross Product and Vector Multiplication

33 views (last 30 days)
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.
  4 Comments
Melissa
Melissa on 19 Aug 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 on 19 Aug 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

Sign in to comment.

Accepted Answer

Roger Stafford
Roger Stafford on 19 Aug 2013
C = [ cross(A',B(:,1)) , cross(A',B(:,2)) , cross(A',B(:,3)) ]\(D');
  4 Comments
Melissa
Melissa on 19 Aug 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 on 19 Aug 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.

Sign in to comment.

More Answers (3)

joseph agno
joseph agno on 7 Oct 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 on 11 Oct 2020
if n corss n = ny
how to write cross in symbol notation form in matlab

muhammad asif
muhammad asif on 11 Oct 2020
circle statement
  1 Comment
Steven Lord
Steven Lord on 11 Oct 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!

Sign in to comment.

Categories

Find more on Performance and Memory in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!