- #1
forty
- 135
- 0
Show that the circle that is in the intersection of the plane x+y+z=0 and the sphere x2+y2+z2=1 can be expressed as:
x([tex]\vartheta[/tex]) = (cos([tex]\vartheta[/tex])-(3)1/2sin([tex]\vartheta[/tex])) / (61/2)y([tex]\vartheta[/tex]) = (cos([tex]\vartheta[/tex])+(3)1/2sin([tex]\vartheta[/tex])) / (61/2)z([tex]\vartheta[/tex]) = -(2cos([tex]\vartheta[/tex])) / (61/2)
I'm really stuck on how to do this. I have already looked over a couple of threads on this forum as well as others however they all do the intersection between a sphere and a plane.
I know this is the unit sphere centered at (0,0,0) and I know the plane is 45 degrees to all axis with its normal vector defined as (1,1,1). I've tried changing co-ordinate systems as well as using some trig substitutions. I've also tried projecting the intersection onto a plane but can't really work out how to do that properly.
Any help on this would be greatly appreciated, thanks!
x([tex]\vartheta[/tex]) = (cos([tex]\vartheta[/tex])-(3)1/2sin([tex]\vartheta[/tex])) / (61/2)y([tex]\vartheta[/tex]) = (cos([tex]\vartheta[/tex])+(3)1/2sin([tex]\vartheta[/tex])) / (61/2)z([tex]\vartheta[/tex]) = -(2cos([tex]\vartheta[/tex])) / (61/2)
I'm really stuck on how to do this. I have already looked over a couple of threads on this forum as well as others however they all do the intersection between a sphere and a plane.
I know this is the unit sphere centered at (0,0,0) and I know the plane is 45 degrees to all axis with its normal vector defined as (1,1,1). I've tried changing co-ordinate systems as well as using some trig substitutions. I've also tried projecting the intersection onto a plane but can't really work out how to do that properly.
Any help on this would be greatly appreciated, thanks!