Finding equation of an invariant line under transformation in 3D.

[Peyman]

Does anyone know how to find the equation of an invariant line in three dimensions under transformation. I know how to find this two dimensions (i.e. equating the gradient and the intercept constants of the original lien to the transformed line) but not sure how to do it in 3D in Cartesian form or vector form.

Best,

Peyman

 

[Deleted member 4993]

Does anyone know how to find the equation of an invariant line in three dimensions under transformation. I know how to find this two dimensions (i.e. equating the gradient and the intercept constants of the original lien to the transformed line) but not sure how to do it in 3D in Cartesian form or vector form.

Best,

Peyman

What is the equation of a straight-line in 3-D?

 

[Peyman]

No, the question is how to find the equation of the lines in 3 dimensions that map to themselves under transformation i.e. invariant lines. This is the actual question: 'Find the equations of lines that map to themselves under the transformation given by the 3x3 matrix [2 0 0; 0 1 0; 0 0 2]'

Best,

Peyman

 

[Deleted member 4993]

No, the question is how to find the equation of the lines in 3 dimensions that map to themselves under transformation i.e. invariant lines. This is the actual question: 'Find the equations of lines that map to themselves under the transformation given by the 3x3 matrix [2 0 0; 0 1 0; 0 0 2]'

Best,

Peyman

Have you done an equivalent problem in 2-D?

If yes, please post the problem and the solution.

 

[topsquark]

No, the question is how to find the equation of the lines in 3 dimensions that map to themselves under transformation i.e. invariant lines. This is the actual question: 'Find the equations of lines that map to themselves under the transformation given by the 3x3 matrix [2 0 0; 0 1 0; 0 0 2]'

Best,

Peyman

I agree with Subhostosh Khan that you should show us how you solved the 2D problem. However I suspect your method for 2D is not the best to use as a general case. Can you write the equation of a line in parametric form?

-Dan