Rotation by matrix multiplication -- confirmation please

[Jamie2020]

Homework Statement

Matrix Rotation

Relevant Equations

0 0 -1
0 1 0
1 0 0

The below matrix represents a rotation.

0 0 -1
0 1 0
1 0 0

Im trying to obtain the general point (x y z) when rotated by the above rotation matrix? So visited https://www.andre-gaschler.com/rotationconverter/ entered the above figures and not sure which entry would be x y z but assume it would be Euler angles (radians) - Could anyone confirm if this would be correct?

Thanks

 

[Zack K]

If you are asking how your coordinates transformed, then you do a matrix multiplication of that with your (x,y,z) column vector and see the result.

 

[Jamie2020]

Sorry not sure i fully understand what your asking me to do? I thought the result was on that link i provided or are you asking me to a particular area?

 

[BvU]

Hi,

Not clear what you mean with 'a general point' in the context of (rotation) matrices.

Your matrix swaps x and z and leaves y unchanged. A positive z ends up pointing in a negative x direction.

A little sketch shows that it is a rotation of the xz plane where the x-axis rotates over an angle ##\pi\over 2## towards the z axis.

 

[kuruman]

Are you looking for a general rotation matrix in terms of Euler angles? If so go here:
https://en.wikipedia.org/wiki/Euler_angles

 

[Jamie2020]

General point is what's written on my paper.

So i assume the answer would be x: 0, y: -1.5707963, z: 0

 

[BvU]

General point is what's written on my paper.

I can't see your paper from here

So i assume the answer would be x: 0, y: -1.5707963, z: 0

That would be a way to describe the rotation: around the y-axis over ##-{\pi\over 2}## (i.e. in mathematically negative direction: clockwise as seen from the tip of the vector looking towards the origin.

 

[Jamie2020]

So changing the above link to degrees would give x: 0, y: -90, z: 0. Unfortunately i copied the question as is so i may need to seek further clarification.

The next 2 related questions are

Next bit is to fill the gaps: The rotation matrix represents A rotation of _________ degrees about the ______ axis.
(I think the first gap is -90 and y (axis)
and

Calculate the single rotation matrix that represents two applications of the above rotation matrix

which i would look into next but not sure if that sheds any light on the first question?

 

[BvU]

The next 2 related questions are

Can you post the full and complete poblem statement ? It is still totally unclear to me what exactly is asked of you (and what you have edited or filled in yourself).
Is 'a general point' actually in the problem text ? Or in the preceding chapter in your textbook or course notes ? If so, how is it defined ?

So changing the above link to degrees

Why would you want to do such a thing ?

Now come the Next bit , apparently litterally copied:

The next 2 related questions are

Next bit is to fill the gaps: The rotation matrix represents A rotation of _________ degrees about the ______ axis.

I agree with your reply.

Calculate the single rotation matrix that represents two applications of the above rotation matrix

Two approaches:
Do you know how to multiply two matrices ?
If you made a sketch of the first rotation, can you visualize the result of a repeat ?