Angle at origin between 3 intersecting planes

[Michael S]

I'm looking for help calculating the angle created between intersecting lines where 3 planes meet (see attached). I would like a formula for omega, wi

 

[stapel]

I'm looking for help calculating the angle created between intersecting lines where 3 planes meet (see attached). I would like a formula for omega, wi

Doesn't the diagram *give* you the value of $\Omega$?

 

[Michael S]

Yes, I'm providing that to show what the correct answer is for the given alpha and beta values. Since alpha and beta change, I need a formula to calculate omega in terms of alpha and beta.

 

[stapel]

Yes, I'm providing that to show what the correct answer is for the given alpha and beta values. Since alpha and beta change, I need a formula to calculate omega in terms of alpha and beta.

The picture has four labelled angles, one of which is $\Omega$. Which of the remaining three are $\alpha$ and $\beta$?

When you reply, please include a clear listing of your thoughts and efforts so far, so the helpers can see where you're having difficulty. Thank you!

 

[blamocur]

Also, some angles are measured between the lines and others between the planes. To avoid unnecessary confusion you might want to be more specific which one is which.

 

[Michael S]

I found this answer on another forum and thought I should post it here. This was very helpful, but was still lacking what I need, so what I'm trying to do may not be possible. The attached is the answer to basically the same question I have, and it also has a good diagram. In my application, I have theta and gamma, and am looking for alpha (according to this diagram). I also have all information associated with triangle OBC. It may be a bit difficult to tell from this diagram, but the third plane is OCD. The lines OA, OB, and AB don't make a plane, they are only there to provide reference for the equations provided. It seems that there would be a way to find beta, given the information I have, but I need help doing that (this is the last piece of info I need to solve for alpha).

 

[blamocur]

The lines OA, OB, and AB don't make a plane,

Any three points (O,A,B in this case) lie on a plane.

Also, where is $\theta$ ?

 

[Michael S]

Theta isn't shown in the diagram, but it's the angle between OA and OB. Theta is a value I know.

 

[blamocur]

I still find this very confusing. What exactly is given, and what needs to be found? The example you found says

I also have all information associated with triangle OBC.

What information?

I honestly tried to figure out the problem statement from your posts, but I cannot. Maybe someone else will have a better luck, but I'll wait until I see the problem stated clearly with a clear diagram.