Rotation Matrix problem

[imDone]

Hello everyone!
This is my first post so please take care of me,

I am having big trouble with the following exercise.


So, I have some possible ways to solve it, but not really sure.
The first one is by using rotation matrix properties: One being that the determinant of a rotation matrix equals 1. But then what?, I have one equation with 4 variables, can't really do anything else.
The other one is that the inverse of a rotation matrix equals it's transposed. Same as before, even if I try to do it i can't get anywhere.

I am also pretty sure that I should be able to compare vectors, or something like that to get several equations, then I guess I could solve it.

Any insight?

Thank you very much!

 

[imDone]

Update on the problem: I found an interesting thingy here



But still do not know how to apply it

 

[Harry_the_cat]

Use the fact that \(\displaystyle R^T = R^{-1}\).

In other words: \(\displaystyle R R^T= I \)

See what that gives you.

 

[imDone]

Can you tell me if I am doing it right? Because I dont have a way to know if I am correct or not:
So, for a1:
a1*a1 + ((-0'2655)x(-0'2655)) + ((-0'2113)x(-0'2113)) = 1
a1 = 0'940671069

If the first one is correct I can assume the rest of operations are correct too,

thanks.

 

[Deleted member 4993]

Can you tell me if I am doing it right? Because I dont have a way to know if I am correct or not:
So, for a1:
a1*a1 + ((-0'2655)x(-0'2655)) + ((-0'2113)x(-0'2113)) = 1
a1 = 0'940671069

If the first one is correct I can assume the rest of operations are correct too,

thanks.

If those 'x' s are supposed to be multiplication sign - use * instead.

Please share your intermediate steps - so that we can correct your error (if any present).

 

[imDone]

So, this is my approach. Because of the A*At = I. I can equal the operation to 1 (the first element of the identity matrix)
Same for the other elements.
Is it ok?

 

[imDone]

Also, I am aware that you usually prefer different problems on different posts. But can you give me a hint on the following one? I could solve it if I had the rotation matrix, but because im missing elements I cant do that.

I hope you can make an exception on this one