# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sun, 19 May 2013 20:52:39 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 5 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Differential Geometry - Line of IntersectionPosted: Tue, 17 Jul 2007 04:43:18 UTC

Joined: Tue, 17 Jul 2007 04:34:16 UTC
Posts: 8
Hi,

I need help with the line of intersection between 2 planes. I am quite embarassed that I don't remember how to do this

I need to find the equation of the plane through (-2,1,-4) which is perpendicular to the line of intersection of the planes 4x + 2y + 2z = -1 and 3x + 6y + 3z = 7.

I am stuck on finding the line of intersection. I have let n1=(4,2,2) and n2=(3,6,3) and have n1xn2=[-6,-6,18] and I now think that I have to let n1=n2 which will give me a point on the line of intersection but I am not too sure how to do it.

Any help appreciated - thanks in advance.
bucjen

Top

 Post subject: Re: Differential Geometry - Line of IntersectionPosted: Tue, 17 Jul 2007 05:52:26 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 14 Jan 2006 22:40:49 UTC
Posts: 694
Location: Yountville, California
bucjen wrote:
Hi,

I need help with the line of intersection between 2 planes. I am quite embarassed that I don't remember how to do this

I need to find the equation of the plane through (-2,1,-4) which is perpendicular to the line of intersection of the planes 4x + 2y + 2z = -1 and 3x + 6y + 3z = 7.

I am stuck on finding the line of intersection. I have let n1=(4,2,2) and n2=(3,6,3) and have n1xn2=[-6,-6,18] and I now think that I have to let n1=n2 which will give me a point on the line of intersection but I am not too sure how to do it.

Any help appreciated - thanks in advance.
bucjen

Let and be any point on the intersection of the two planes (i.e., it satisfies the two equations). Then the line of intersection is the set of points of the form for . The plane you want has normal and its equation is where and .

Last edited by Bilbo on Mon, 7 Mar 2011 10:24:09 UTC, edited 1 time in total.

Top

 Post subject: Posted: Tue, 17 Jul 2007 06:01:35 UTC

Joined: Tue, 17 Jul 2007 04:34:16 UTC
Posts: 8
Hey Bilbo

I guess the trouble I am having is finding points to satisfy both equations. Can you help with that?

Thanks
bucjen

Top

 Post subject: Posted: Tue, 17 Jul 2007 06:51:26 UTC
 Senior Member

Joined: Wed, 27 Jun 2007 09:10:55 UTC
Posts: 66
To find the equation of the line, solve the system with unknown and as parameter.
We get .
Then we can write or
.
So the director vector of the line is which it is also the normal vector of the plane.
Then the equation of the plane passing through the point is

Top

 Post subject: Posted: Tue, 17 Jul 2007 07:30:36 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 14 Jan 2006 22:40:49 UTC
Posts: 694
Location: Yountville, California
bucjen wrote:
Hey Bilbo

I guess the trouble I am having is finding points to satisfy both equations. Can you help with that?

Thanks
bucjen

Notice that the equation of the plane doesn't make any reference to a point on the line. All you need is the normal , which you calculated from the cross product, and the point you want the plane to go through. Also notice that the only calculation you need is the cross product.

If you need to find points on the line in addition to the equation of the plane, red_dog shows you how to do that. red_dog's calculation yields an equation for the plane that is a multiple (-6) of the one I give.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 5 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous