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 3 years ago
Give the formulae for the transformation of the coordinates of a vector. Plssssssss
 3 years ago
Give the formulae for the transformation of the coordinates of a vector. Plssssssss

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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.
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