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

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Stanley Cheng 2013-12-17

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评论： Jeff 2014-12-4

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!

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采纳的回答

Matt J 2013-12-17

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编辑：Matt J 2013-12-17

在 MATLAB Online 中打开

null(r1(:).')

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Matt J 2013-12-17

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 2014-12-4

AWESOME!

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David Sanchez 2013-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/110051-how-to-obtain-the-orthogonal-vectors-of-one-3-1-unit-vector#answer_118663

在 MATLAB Online 中打开

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

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Matt J 2013-12-17

在 MATLAB Online 中打开

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

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