- #1
jemck
- 2
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It has been a while and trying to brush up on LaGrange points. I want to find the highest and lowest points on the ellipse of the intersection of the cone: x^2+y^2-z^2 ;subject to the single constraint: x+2y+3z=3 (plane).
I want to find the points and I am not concerned with the minimum and maximum yet. So far, I have done the following:
delf<x,y,z>= lambda(del)g<x,y,z>
<2x,2y.-2z>= lambda<1,2,3> where g(x,y,z)=3
Hence, 2x=1*lambda or (2x-1*lambda)=0
2y=2*lambda or (2y-2*lambda)=0
-2z=3*lambda or (-2z-3*lambda)=0
Furthermore, lambda=2x x=lambda/2
lambda=y or y=lambda
lambda=(-2/3)*z z=(-3/2)*lambda
Solving the systems I guess would be my area of problems. or putting things together: Using the constraint as a guideline, and solving for lambda, I obtain that lambda=7/3.
And, if lambda=7/3 x=7/6
y=7/3
z=-7/2
I would say that I am at the final steps of obtaining my points for the function; however, I am confusing myself with what points are permissible. ie.: (0,0,-7/2)
(0,7/3,0)
(7/6,0,0)
See what I am getting at? I would appreciate any guidance to putting this puzzle together
I want to find the points and I am not concerned with the minimum and maximum yet. So far, I have done the following:
delf<x,y,z>= lambda(del)g<x,y,z>
<2x,2y.-2z>= lambda<1,2,3> where g(x,y,z)=3
Hence, 2x=1*lambda or (2x-1*lambda)=0
2y=2*lambda or (2y-2*lambda)=0
-2z=3*lambda or (-2z-3*lambda)=0
Furthermore, lambda=2x x=lambda/2
lambda=y or y=lambda
lambda=(-2/3)*z z=(-3/2)*lambda
Solving the systems I guess would be my area of problems. or putting things together: Using the constraint as a guideline, and solving for lambda, I obtain that lambda=7/3.
And, if lambda=7/3 x=7/6
y=7/3
z=-7/2
I would say that I am at the final steps of obtaining my points for the function; however, I am confusing myself with what points are permissible. ie.: (0,0,-7/2)
(0,7/3,0)
(7/6,0,0)
See what I am getting at? I would appreciate any guidance to putting this puzzle together