Perform Gram Schmidt orthogonalization in MATLAB

I have three columns of vectors, representing three points in a rigid body, I want to reconstruct a fourth column of vectors, where the relation from the fourth column vector to the remaining three column of vectors are known. I have heard that Gram-Schmidt orthogonalization is the best process since it's algorithm would create a fourth column of vectors, assuming that it is a rigid body. I have attached an image for your help. Thank You!

Answer 1

[Matt J]

The ORTH command or QR command are probably the best for orthogonalization, in general.

If you already have 3 linearly independent vector in 3D space, there is no way to obtain a 4th vector in 3D space that is linearly independent of the other three, if that's what you were trying to do. That would violate laws of linear algebra.

[Matt J]

in your diagram, it just looks like you are being asked to solve for 'f'. With R known, it would just be

f=R\(p4-p1)

[Aviroop Dutt Mazumder]

Thanks Matt, the vectors are not linearly independent in 3-D space. Are you aware of any command that would compute the 4th vector in 3D, based on the remaining four vectors in MATLAB?

[Matt J]

Have you tried

f=R\(p4-p1)