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 25,913
    Science Advisor
    Homework Helper

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

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

    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 25,913
    Science Advisor
    Homework Helper

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