MHB Applying rotation matrix to make inclined plane flat again

[Maestroo]

I want to rotate an inclined plane to achieve a flat surface.
I think I can use the Euler angles to perform this operation.

Using following data:

and following rotation matrix

I think you can make the plane flat by following rotations:
1: rotation around x-axis by 45°
2: rotation around y-axis by -45°
3: no rotation around z-axis

filling in the rotation matrix:

new Z matrix derived from 3rd row: newZ=-X*cosd(45)*sind(-45)+Y*sind(45)+Z*cosd(45)*cosd(-45);

I expect a zero matrix, but this is not the case?
What am I doing wrong?

Thank you

 

[I like Serena]

I want to rotate an inclined plane to achieve a flat surface.
I think I can use the Euler angles to perform this operation.

Using following data:

and following rotation matrix

I think you can make the plane flat by following rotations:
1: rotation around x-axis by 45°
2: rotation around y-axis by -45°
3: no rotation around z-axis

Hi Maestroo! Welcome to MHB! ;)

I'm afraid those are not the correct angles.
From those matrices with points, we can find vectors in the plane, and from those we can find a normal vector to the plane.
The normal vector is $(1,1,1)$.
Did you find that as well?

So we want to find a rotation that rotates $(1,1,1)$ to the z-axis.
Preserving the length, that means rotating it to $(0,0,\sqrt 3)$.
Your approach works, but we'll need to find the proper angles.
First we would rotate $(1,1,1)$ around the x-axis to some $(x,0,z)$.
And then we would rotate $(x,0,z)$ around the y-axis to $(0,0,\sqrt 3)$.
However, those angles are not $45^\circ$.
We might use the dot product to figure out the correct angles, while preserving lengths and angles. (Thinking)

For the record, we can also follow a different approach that doesn't use Euler angles.

 

[Maestroo]

Ok thank you alread

I found out that the shown rotation matrix is for fixed XYZ axes (not relative), I will update later which rotation matrix I'm now using.

I found out the correct 2nd angle by drawing:
rotations - GeoGebra

Now I will search for the way to find this angle.