Results 1 to 2 of 2

Math Help - Vectors Help

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    22

    Vectors Help

    am looking over a solution to an answer and i dont get some things

    Question is

    Find the distance from the point A(1,-2,3) to the plane 2x-3x+6z-8=0

    Then they picked a random point
    P(4,0,0)
    and AP=(3,2,-3)

    However they also got a vector n=(2,-3,6)

    That vector is included in
    |AH|=proj n(PA)

    =PA*n/n*n |n|

    That turns out to be
    (3,2,-3)*(2,-3,6) ALL OVER (2,-3,6)*(2,-3,6)
    all times sqrt 2^2 +(-3)^2+6^2


    My question is how did they get that point n?
    Where could that have come from?
    Thank you for your help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    Here is the situation


    n is a normal vector to the plane
    For a plane ax+by+cz+d=0, we know that a normal vector has coordinates (a,b,c)

    P is a point picked at random on the plane
    H is the projection of A on the plane
    The distance from A to the plane is AH

    The dot product of AP and n is
    AP.n = (AH+HP).n = AH.n + HP.n = AH.n since HP and n are perpendicular
    |AP.n| = |AH.n| = AH ||n|| since AH and n are parallel

    AH = |AP.n| / ||n||
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 06:10 PM
  2. Replies: 3
    Last Post: June 30th 2011, 09:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 11:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2011, 01:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 07:03 PM

Search Tags


/mathhelpforum @mathhelpforum