A community for students.
Here's the question you clicked on:
 0 viewing
atjari
 3 years ago
Give the formulae for the transformation of the coordinates of a vector. Plssssssss
atjari
 3 years ago
Give the formulae for the transformation of the coordinates of a vector. Plssssssss

This Question is Closed

saljudieh07
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, I have no idea

atjari
 3 years ago
Best ResponseYou've already chosen the best response.0Ha k. Cn any1 else help me.?

bahrom7893
 3 years ago
Best ResponseYou've already chosen the best response.0transformations into what?

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0are you talking about linear transformations: R2 > R3 ??

saljudieh07
 3 years ago
Best ResponseYou've already chosen the best response.0does this help? http://en.wikipedia.org/wiki/Transformation_matrix

atjari
 3 years ago
Best ResponseYou've already chosen the best response.0It's a part of a question. Let me type the whole question.

atjari
 3 years ago
Best ResponseYou've already chosen the best response.0Pls see the attachment for the full question.

opiesche
 3 years ago
Best ResponseYou've already chosen the best response.2Part of forming a basis is that the vectors u,v,w have to be linearly independent. That means that each of the vectors can't be a linear combination of the others. So, let's look at the new vectors (let's call them x,y,z) x = u+v y = u+w z = u+v+w If you take any of x,y and z, and linearly combine them, can you end up with another one of x, y or z (hint: you can't)? If not, x, y and z form a basis. As for the second part of the question, are we talking affine transformation? Those are most easily expressed in a matrix, which reduces the transform to a vectormatrix multiply (which itself is just a series of dot products). I'm not sure what formulae are being looked for here, because it depends on the transform asked for. If it's just a rotation, it's relatively simple  you can just build a matrix like so: \[\left[\begin{matrix}\cos \beta \cos \gamma & \cos \alpha \sin \gamma + \sin \alpha \sin \beta \cos \gamma & \sin \alpha \sin \gamma + \cos \alpha \sin \beta \cos \gamma\\ \cos \beta \sin \gamma & \cos \alpha \cos \gamma + \sin \alpha \sin \beta \sin \gamma & \sin \alpha \cos \gamma + \cos \alpha \sin \beta \sin \gamma \\ \sin \beta & \sin \alpha \cos \beta & \cos \alpha \cos \beta\end{matrix}\right]\] where \[\alpha, \beta, \gamma\] are Euler angles (rotations about the X, Y, and Z axes of your coordinate system), respectively. A multiplication of a 3vector with such a matrix would yield a 3vector rotated by the three angles. It follows, that for example to get the transformed xcomponent of the vector v [xyz], you would calculate \[x' = x*cos \beta cos \gamma + y*cos \beta sin \gamma + z*sin \beta \] And do similarly for the y and z components with the second and third column of the matrix. Someone please double check my math here, it's been a while since I've actually built a rotation matrix by hand :P

atjari
 3 years ago
Best ResponseYou've already chosen the best response.0Thanx a lot for this great help.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.