Find parametric question for the plane

  1. 1. The problem statement, all variables and given/known data
    Give parametric questions for the plane : 2x-3y+z-6=0


    3. The attempt at a solution

    i know that the normal is (2,-3,1)
    how do i find the direction vector of the plane?
     
  2. jcsd
  3. Dick

    Dick 25,824
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    The plane has two linearly independent 'direction vectors'. Find any two independent vectors perpendicular to your normal.
     
  4. HallsofIvy

    HallsofIvy 40,391
    Staff Emeritus
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    Dick is assuming that by 'direction vector', you mean two independent vectors in the plane. I've only seen the term used with lines.

    I wonder if you are not confusing this with "find the parametric equations for a line". To do that you would find 'direction vector' for the line. Parametric equations for a plane will involve two parameters. Here, since you can write z as a function of x and y, z= 6- 2x+ 3y, you can use x and y themselves as parameters or, if you prefer distinct variables, x= u, y= w, z= 6- 2u+3w.
     
  5. Dick

    Dick 25,824
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    That's a much more direct way. I was fixated on the 'direction vector' (basis) picture.
     
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