How to form the transformation matrix for this

AI Thread Summary
The discussion revolves around forming a transformation matrix to rotate the x1 axis of a rectangular coordinate system by 60 degrees towards the x2 and x3 axes. Participants express confusion over the interpretation of "rotating one axis toward the two others," questioning whether it means rotating towards the x2-x3 plane or in relation to each axis separately. It is noted that there are multiple ways to achieve this rotation, depending on which axis is fixed during the transformation. Ultimately, clarification from the teacher revealed that the rotation should be around the x3 axis, simplifying the problem. The conversation highlights the importance of precise language in mathematical problems to avoid misinterpretation.
Byang
Messages
2
Reaction score
0
We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis.
The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or does it mean something else? I tried to rotate x1 to the x2-x3 plane but I can never be sure of the angle between x1' and x2, and x1' and x3. How do I find the angles?
 
Mathematics news on Phys.org
Byang said:
We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis.
The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or does it mean something else? I tried to rotate x1 to the x2-x3 plane but I can never be sure of the angle between x1' and x2, and x1' and x3. How do I find the angles?

There are infinitely many possible ways of rotating the ##x_1## axis by ##60^o## towards the ##x_2-x_3## plane. For example, you could fix ##x_2 = 0## and rotate the ##x_1## axis towards the ##x_3## axis, or fix ##x_3 = 0## and rotate ##x_1## towards ##x_2##, etc. In all these cases you would be rotating ##x_1## by ##60^o## towards the ##x_2-x_3## plane. In general, you could fix an arbitrary point ##p = (0,p_2,p_3)## in the ##x_2-x_3## plane, and rotate the ##x_1## axis towards ##p##.

Basically, I don't know exactly what your question wants; perhaps they mean ##60^o ## towards ##x_2## and then ##60^o## towards ##x_3##, or maybe they mean two separate questions---one for an ##x_1 \to x_2## rotation and another for an ##x_1 \to x_3## rotation.
 
Ray Vickson said:
Basically, I don't know exactly what your question wants
Haha, that's exactly my problem. But thank you for answering. We've cleared it up with our teacher and she said it was supposed to be "around x3 axis," which makes the problem a lot easier.
 
Thread moved as it seems to be more of a general question than a specific homework problem.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Maximizing x1+1.2*x2+1.5*x3 subject to Constraints | Linear Equations
Replies
22
Views
5K
How to determine if a transformation is linear
Replies
26
Views
3K
Algorithm problem involving 3 points and 3 lines in the x,y plane
Replies
7
Views
2K
B How to find the infinitesimal coordinate transform along a hyperbola?
Replies
1
Views
1K
A Simple question on the derivative of base frame
Replies
1
Views
2K
I Cartesian to Polar form.... Is it just a transformation of the plane?
Replies
8
Views
2K
Solving a Matrix: Finding Positive & Negative Solutions
Replies
1
Views
2K
A Connection between 1-Forms and Fourier Transform
Replies
3
Views
3K
Express the system in state space form
Replies
2
Views
2K
I Transforming coordinates between Cartesian and spherical
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top