Results 1 to 3 of 3
Like Tree2Thanks
  • 2 Post By HallsofIvy

Thread: Unit normal vector

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    41

    Unit normal vector

    Good morning,

    Given 3 points, I must find the unit normal vector for the best fit plane through them. The plane must also include the origin (0,0,0)

    Can someone give me a hand?

    Kind regards,

    Kepler
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,811
    Thanks
    1921

    Re: Unit normal vector

    What are the three points?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,029
    Thanks
    2765

    Re: Unit normal vector

    Three points determine a plane. Given three points, P, Q, and R, construct the two vectors \vec{PQ} and \vec{PR} that lie in that plane. The cross product of the two vectors is normal to the plane. If that normal vectors is A\vec{i}+ B\vec{j}+ C\vec{k} and any one of the three points is (x_0, y_0, z_0) then the eqation of the plane is A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0 and the unit normal vector is \frac{1}{\sqrt{A^2+ B^2+ C^2}}\left(A\vec{i}+ B\vec{j}+ C\vec{k}\right).
    Thanks from topsquark and kepler
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: Oct 26th 2016, 06:58 AM
  2. Replies: 5
    Last Post: Jul 25th 2016, 02:32 PM
  3. Replies: 3
    Last Post: Oct 22nd 2012, 08:57 AM
  4. Unit Normal Vector
    Posted in the Calculus Forum
    Replies: 9
    Last Post: Jun 13th 2011, 06:04 AM
  5. unit normal vector
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 21st 2009, 07:59 AM

/mathhelpforum @mathhelpforum