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Simple question about parametric equations of a plane in 3D

  1. Nov 7, 2013 #1
    I'm quite rusty in Linear Algebra.

    If you have a plane in 3D with the equation ##z=2##, what does ##x## and ##y## equal? Does ##x=t## and ##y=t##?

    Because if I graph that in Wolfram Alpha, I don't get a horizontal plane in 3D at ##z=2##: http://www.wolframalpha.com/input/?i=graph+z=2,x=t,y=t
     
  2. jcsd
  3. Nov 7, 2013 #2

    tiny-tim

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    hi ainster31! :smile:
    line: one parameter

    plane: two parameters :wink:

    your plane is z = 2, x = t, y = u​
     
  4. Nov 7, 2013 #3
    Hmm... what about 3 parameters? What would that result in? A filled 3D cube, right?
     
  5. Nov 7, 2013 #4

    Mark44

    Staff: Mentor

    If x, y, and z are arbitrary, you get the entire space (all of R3).
     
  6. Nov 7, 2013 #5

    tiny-tim

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    3 dimensions: 3 parameters …

    n dimensions: n parameters …

    that's very nearly a definition of dimensions! :smile:
     
  7. Nov 9, 2013 #6
    z=2 is the equation of a plane in R^3. x and y range over R since they are not specified. So you essentially end up with an x,y plane. In wolfram alpha they just show a line since there doesn't appear to be an easy way to tell it you want R^3. Your initial assumption was correct and variable t shouldn't be introduced.
     
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