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Combining Parametric Equations

  1. Jan 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation
    5x - 3y - z - 6 = 0

    2. Relevant equations

    3. The attempt at a solution

    So what I did was solve the equation v by adding the x,z,and z components to get

    x = 1 + 2t
    y = -1 + 3t
    z = 2 + t

    So I'm thinking that if I can combine these into one equation that I would end up getting the answer. Problem is I can't figure out how to combine the three equations in an equation with all three variables. I keep getting the function in terms of two variables, or the wrong answer all together. One method I used was solving the z equation for t and then plugging it into the x equation and then the y equation. I tried setting they both equal to zero...

    t = z -2
    y = 3z-7 y - 3z + 7 = 0
    x = 2z-3 x - 2z + 3 = 0

    y - 3z + 7 = x -2z + 3

    y - z - x + 4 = 0

    Obviously this isn't the correct answer. What am I doin' wrong here?
  2. jcsd
  3. Jan 9, 2008 #2


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    Homework Helper

    Just put your parametric t expressions for x,y and z into 5x-3y-z-6. Do you get zero?
  4. Jan 10, 2008 #3
    Cool... that works. Why didn't my method work also? Is there more than one equation that can solve that parametric equation?
  5. Jan 10, 2008 #4
    Stupid answer goes here.
    Last edited: Jan 10, 2008
  6. Jan 10, 2008 #5
    Was my algebraic logic correct though? The answer I got was not off by a constant.
  7. Jan 10, 2008 #6
    Never mind, I'm an idiot. A line doesn't determine a plane. Wow. Your work is fine, it's just you found a plane that the line is in that isn't the plane you started with.
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