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Parametric line

  1. Aug 17, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem is pretty simple but I seem to be missing something essential .Write parametric equation of line which passes through point P0(1,-1,-3) and is parallel with line (x+1)/1=(y+2)/4=(z-1)/0

    2. Relevant equations
    solutions are x=2t+1 ,y=4t-1,z=-3

    3. The attempt at a solution
    I would really really appreciate if u could simply say the magic word because this looks really easy but yet troubling to my brain I think Im tired !
  2. jcsd
  3. Aug 17, 2010 #2


    Staff: Mentor

    If you know a point on a line and a vector parallel to the line, can you get the parametric equations for the line?

    You can extract the coordinates of a vector from the symmetric equations (x+1)/1=(y+2)/4=(z-1)/0; namely <1, 4, 0>.

    That should get you started.
  4. Aug 17, 2010 #3


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    Homework Helper

    What is the direction of this line?
  5. Aug 18, 2010 #4
    And you're Awesome !!
  6. Aug 18, 2010 #5


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    Science Advisor

    In general, any line parallel to
    [tex]\frac{x- x_0}{A}= \frac{y- y_0}{B}= \frac{z- z_0}{C}[/tex]

    and passing through the point [itex](x_0, y_0, z_0)[/itex] is of the form
    [tex]\frac{x-x_1}{A}= \frac{y- y_1}{B}= \frac{z- z_1}{C}[/tex]

    That is, it is precisely the numbers A, B, C that determine the direction.
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