Orthogonal vectors, how to code?

Hi,

I am trying to put in my code that two vectors w⃗ = (w1, w2, w3) and ⃗v = (v1, v2, v3), with the lenght of 1, are orthogonal to each other and have the first coordinate 0. I am able to solve this as an equation system on paper but I am also tying to solve it in matlab. I have come up with the following, but I do not know how to say that the vectors are orthogonal to each other. Any ideas?

v1 = [0 u(3) u(2)];
v1 = v1 / norm(v1);

[Steven Lord]

Editing away your questions, as you did with your previous question, means that others can't learn from that discussion. What guarantee do I have that if I were to answer you wouldn't simply edit away this question?

[Jenny Andersen]

Sorry about that! I will try and fix it.

[Jan]

I do not undestand the question. Do you want to check if the vectors are orthogonal or do you want to create an orthogonal vector?

Two vectors [w1, w2, w3] and [v1, v2, v3] with w1=0 and v1=0 are orthogonal, if w2*v2 + w3*v3 == 0.

Answer 1

[Matt J]

Any two such vectors will have this parametric form,

w=  [0 cos(theta) sin(theta)]
v=c*[0 -sin(theta) cos(theta)]

where c=+1 or -1.