Results 1 to 2 of 2

Math Help - equations of planes

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    5

    Question equations of planes

    There are three coordinates planes in 3-space. A line in R^3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R^3. Support your answer using examples.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    I'm not sure I understand the question! "Explain what this tells you about parametric and symmetric equations in R^3." It doesn't tell you anything about them in general! Did you mean, "Explain what this tells you about parametric and symmetric equations of this line in R^3"?

    If a line is parallel to the xy-plane, then z does not change. The parametric equations will have z= constant. The requirement that it not be parallel to any axis just says that x and y do change. Typically the way you form the "symmetric equations" from the parametric equations is to solve each equation for the parameter, then set them all equal. Since here, z is a constant, there is no parameter in that equation and so you cannot solve for it. The "symmetric equations" will be just a single equation in x and y, with the additional equation z= constant. Geometrically, you can think of this as the a line in xy-plane "shifted" up or down along the z-axis.

    It's easy to make up examples. Just write "x= f(t), y= g(t), z= c" where f(t) and g(t) are any linear functions you want to use and c is any constant.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equations of Planes 2
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 13th 2009, 07:55 AM
  2. Equations of Planes 5
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 12th 2009, 12:50 PM
  3. Equations of Planes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 11th 2009, 05:31 PM
  4. Planes in 3-space; Equations of planes
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: July 30th 2008, 03:01 PM
  5. equations planes
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 29th 2007, 11:26 AM

Search Tags


/mathhelpforum @mathhelpforum