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Find parametric representation for the plane

  1. Mar 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Plane: 4x−2y+10z =16.

    2. Relevant equations



    3. The attempt at a solution

    So I've used two parameters, "u" and "v" with x = u and y = v
    Re-arranging z in terms of "u" and "v": z = 1.6 - 0.4x + 0.2y
    Hence r(t) = (u , v , 1.6 - 0.4 x + 0.2y)
    Is this correct?
     
  2. jcsd
  3. Mar 13, 2013 #2

    vela

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    Essentially. x and y shouldn't be in your final expression; there should only be u and v.
     
  4. Mar 13, 2013 #3
    oh yeah, sorry was a typo
    but anyway, the solutions say the answer is (10u,10v,−4u+2v+1.6)
    which isnt equivalent to my answer...
     
  5. Mar 13, 2013 #4

    vela

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    They're equivalent. The solutions defined the parameters as x=10u and y=10v.
     
  6. Mar 14, 2013 #5
    ah I see, thanks!
     
  7. Mar 15, 2013 #6

    HallsofIvy

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    Personally, I would have got a third answer!
    We can easily solve 4x- 2y+ 10z= 16 for y: y= 2x+ 5z- 8.

    Now, use x and z as parameters:
    x= u
    y= 2u+ 5v- 8
    z= v
     
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