Results 1 to 3 of 3

Math Help - parametric description of plane help

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    146

    parametric description of plane help

    if c is the plane through the following points
    (0,1,1) (0,1,0) and (-2,-1,-1)

    how can I find an equation and parametric description of the plane?

    I know the equation of the plane can be written as

    a(x-x0) + b(y-y0) +c(z-z0) for a point (x0,y0,z0) and a normal vector (a,b,c)

    how can I find the normal vector from the points?
    I am also not sure about the difference the equation and parametric representation

    thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,367
    Thanks
    1312

    Re: parametric description of plane help

    The vector from point (x_0, y_0, z_0) to (x_1, y_1, z_1) is <x_1- x_0, y_1- y_0, z_1- z_0>. So two vectors in the plane are the vector from (0, 1, 1) to (0, 1, 0), <0- 0, 1- 1, 0- 1>= <0, 0, -1> and the vector from (0, 1, 1) to (-2, -1, -1), <0-(-2), 1-(-1), 1-(-1)>= <2, 2, 2>.

    A vector perpendicular to those two vectors, and so perpendicular to the plane is their cross product.

    A two dimensional surface in a three dimensional space can be written as a single equation, z= f(x,y) or, more generally, g(x,y,z)= constant. A plane can be written as a linear equation, say, ax+ by+ cz= d for some constants, a, b, c, and d. Parametric equations, in three dimensions, are three equations x= f(t), y= g(t), z= h(t) for a one dimensional figure (a curve or line) or x= f(s, t), y= g(s,t), z= h(s,t) for a two dimensional figure (the number of parameters is the dimension). A plane can be written in linear equations: x= as+ bt+ c, y= ds+ et+ f, z= gs+ ht+ i.

    Given a surface given by the single equation, z= f(x,y), you can always take x and y themselves as parameters: x= s, y= t, z= f(s, t).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    Posts
    146

    Re: parametric description of plane help

    thanks for the help. I managed to get the normal vector as (2,-2,0)

    I have another question


    I have a normal vector (2,-2,0) of the plane and a point on a line orthogonal to the plane. (4,0,1). So my goal is to try and find the parametric description of this line.
    now to do that I need a vector v, but how can I find this vector with the given info?

    the parametric representation is given by p + tv where p is a point and v is a vector. I need another point on this line to find the vector. Since this line is orthogonal to the plane I know that this vector shoukd be parallel to the normal vector of the plane. But im having difficulty trying to find another point on this line.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parametric equations for a plane parallel
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 4th 2011, 03:15 AM
  2. Parametric equations of the plane
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 2nd 2011, 07:42 AM
  3. Parametric equation of plane
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 6th 2011, 12:38 PM
  4. Write the Plane (Parametric)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2009, 05:19 PM
  5. Parametric Plane Equation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 21st 2008, 12:40 PM

/mathhelpforum @mathhelpforum