FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » Undergraduate
Distance from a Sphere
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
Author Message
Brian
science forum beginner


Joined: 16 May 2005
Posts: 45

PostPosted: Sun Jun 11, 2006 6:48 pm    Post subject: Distance from a Sphere Reply with quote
Hi everyone,

can anyone tell me how to locate the point on the sphere with the equation
x^2 + y^2 + z^2 + 2x - 2y - 4z - 3 = 0 which is closest to the origin ??

Any help much appreciated !!!

Thanks

Brian
Back to top
G.E. Ivey
science forum Guru


Joined: 29 Apr 2005
Posts: 308

PostPosted: Sun Jun 11, 2006 6:58 pm    Post subject: Re: Distance from a Sphere Reply with quote
Quote:
Hi everyone,

can anyone tell me how to locate the point on the
sphere with the equation
x^2 + y^2 + z^2 + 2x - 2y - 4z - 3 = 0 which is
closest to the origin ??

Any help much appreciated !!!

Thanks

Brian

Do you know how to find the center of the sphere?
Write this as (x^2+ 2x+ )+ (y^2- 2y+ )+ (z^2-4z+ )= 3 and complete the square in each part so you get
(x- x_0)^2+ (y- y_0)^2+ (z- z_0)^2= R^2.

The line from the center, (x_0,y_0,z_0), to (0,0,0) passes through the sphere at the point closest to (0,0,0).
Back to top
Paul Sperry
science forum Guru


Joined: 08 May 2005
Posts: 371

PostPosted: Sun Jun 11, 2006 9:43 pm    Post subject: Re: Distance from a Sphere Reply with quote
In article
<2545127.1150051755803.JavaMail.jakarta@nitrogen.mathforum.org>, Brian
<fdbsj453fgjer@yahoo.com> wrote:

Quote:
Hi everyone,

can anyone tell me how to locate the point on the sphere with the equation
x^2 + y^2 + z^2 + 2x - 2y - 4z - 3 = 0 which is closest to the origin ??

Any help much appreciated !!!

Thanks

Brian

If you know the technique, this is a more or less classic Lagrange
multiplier problem:

Minimize x^2 + y^2 + z^2 subject to the constraint
x^2 + y^2 + z^2 + 2x - 2y - 4z - 3 = 0.

G. E. Ivey's suggestion also works fine.

--
Paul Sperry
Columbia, SC (USA)
Back to top
Brian
science forum beginner


Joined: 16 May 2005
Posts: 45

PostPosted: Mon Jun 12, 2006 11:09 am    Post subject: Re: Distance from a Sphere Reply with quote
Thank you for your replies.

They have helped !

Brian
Back to top
Google
Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
The time now is Sat Jan 10, 2009 2:18 am | All times are GMT
Forum index » Science and Technology » Math » Undergraduate
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Instantaneous Action at a Distance Phil Gardner Research 1 Mon Jul 17, 2006 3:32 pm
No new posts distance matrix consolidation bird Math 6 Sat Jul 15, 2006 9:05 pm
No new posts distance between sets diegotorquemada@yahoo.com Math 2 Thu Jul 13, 2006 4:47 pm
No new posts Disconnecting the sphere jn Math 1 Tue Jul 11, 2006 1:52 pm
No new posts Maximum number of small spheres that ... Hyped Math 14 Thu Jun 29, 2006 2:32 pm

Credit Cards | MPAA | Credit Counseling | Car Loan | W810i
Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums


Powered by phpBB © 2001, 2005 phpBB Group

[ Time: 0.5425s ][ Queries: 16 (0.4188s) ][ GZIP on - Debug on ]