Results 1 to 2 of 2

Math Help - Finding Equation of Plane given basis and a point

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    IL
    Posts
    1

    Finding Equation of Plane given basis and a point

    The way that I was taught to find the equation of a plane was to take the cross product of basis vectors (v1 X v2)
    to get a vector that is normal to the plane, and then take the dot product between that vector and P-P0, with P = <x,y,z> and P0 being the position vector of
    another point on the plane. The result would be the equation.


    However, given the basis of the plane (v1, v2).. P-P0 should be expressible as the sum of the basis vectors:


    P - P0 = a*v1 + b*v2


    Is it possible to use this system to find the equation of the plane (z = f(x,y)) with some kind of traditional method (Gaussian elimination)? I think I'm missing a basic idea. Shouldn't this system be a sufficient restriction? Why is the cross product/dot product method necessary?

    Thanks in advance for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,619
    Thanks
    592

    Re: Finding Equation of Plane given basis and a point

    Hey Laffytaffy.

    Note that if you have a plane in teorms of n . (r - r0) where n is the plane normal, r is a general point on the plane and r0 is a specific point, then you can expand this to get ax + by + cz + d = 0.

    Re-arranging this gives you the function z = 1/c*[-ax - by - d] = f(x,y)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 14th 2011, 06:05 PM
  2. Replies: 2
    Last Post: March 1st 2011, 07:57 PM
  3. Point-Normal equation of a plane.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 29th 2011, 01:09 PM
  4. Finding the equation for a plane with only one point
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 24th 2010, 06:30 AM
  5. Replies: 0
    Last Post: May 12th 2010, 05:09 AM

Search Tags


/mathhelpforum @mathhelpforum