Results 1 to 2 of 2

Thread: Equation of planes

  1. #1
    Junior Member
    Joined
    Nov 2012
    From
    england
    Posts
    29

    Equation of planes

    Hi, can anyone explain to me why the equation for a plane3 which contains the intersection line of 2 other planes(plane1 and plane2), is the sum of the equations of plane 1 and plane 2?

    Note the planes all go through the origin.

    ie, if plane 1 is ax+by+cz=0 and if plane 2 is dx+ey+fz=0

    any plane containing the intersecting lines of plane 1 and plane 2 is:

    (a+d)x + (b+e)y + (c+f)z = 0

    Why?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,797
    Thanks
    2828
    Awards
    1

    Re: Equation of planes

    Quote Originally Posted by darren86 View Post
    Hi, can anyone explain to me why the equation for a plane3 which contains the intersection line of 2 other planes(plane1 and plane2), is the sum of the equations of plane 1 and plane 2?

    Notation: $\displaystyle \mathcal{R}=<x,y,z>$ and $\displaystyle P$ is a point.

    Here are two planes $\displaystyle N\cdot(\mathcal{R}-P)=0~\&~M\cdot(\mathcal{R}-P)=0,~N\not \parallel M,$ both containing $\displaystyle P$. The normals are $\displaystyle N~\&~M$

    The equation of the line of their intersection is $\displaystyle P+t(N\times M)$.

    Because $\displaystyle (N+M)\cdot(N\times M)=0$ means the plane $\displaystyle (N+M)\cdot(\mathcal{R}-P)=0$ contains the line of intersection and has normal $\displaystyle N+M$.

    NOTE that answer is not unique. But it explains your question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Planes and parametric equation
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Oct 10th 2012, 07:40 AM
  2. Planes and parametric equation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Oct 10th 2012, 07:40 AM
  3. Cartesian equation of planes?: Pls help
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Feb 23rd 2010, 01:58 AM
  4. vector help-->equation of planes
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jun 10th 2009, 02:45 PM
  5. Parametric equation of lin eof intersection of two planes?
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Apr 25th 2009, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum