how to obtain the orthogonal vectors of one 3*1 unit vector?

Hi everyone,

I have a 3*1 unit vector as r1= [ 0.6619 0.6976 -0.2740]', and want to obtain the other two unit orthogonal vectors of r1. these two vectors are named as r2 and r3, they satisfy:

R=[r1 r2 r3] is a 3*3 unit orthogonal matrix.

Could anyone tell me what commands in matlab is useful to do this? Thx very much!

Answer 1

[Matt J]

null(r1(:).')

[Stanley Cheng]

i find svd is also okay to do this!

[Matt J]

Yes. If you look inside null.m you will see that it uses SVD, but with thresholding rules that you may not agree with.

[Jeff]

AWESOME!

Answer 2

[David Sanchez]

a = [0.6619 0.6976 -0.2740];
b = [a(1) a(3) -a(2)];
c = cross(a,b);
c = c/norm(c);
M = [a;b;c]; % orthogonal matrix

[Matt J]

Don't think so

   >> M'*M

ans =

      1.2669    0.0854   -0.1959
      0.0854    0.6590   -0.2232
     -0.1959   -0.2232    1.0738