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Line passes through a point parallet to parametric equations

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider the line which passes through the point P(-1, 4, 3), and which is parallel to the line x = 1 + 3t, y = 2 + 4t, z = 3 + 5t
    Find the point of intersection of this new line with each of the coordinate planes:
    xy-plane: ( , , 0 )
    xz-plane: ( , 0 , )
    yz-plane: ( 0 , , )


    2. Relevant equations



    3. The attempt at a solution
    I can figure out the whole intersection thing, I just don't understand how I'm suppose to make it parallel to a line at the same time.
     
  2. jcsd
  3. Sep 15, 2009 #2

    Mark44

    Staff: Mentor

    I think you're approaching this in the wrong order. First, find the parameteric equations for the line through (-1, 4, 3), then figure out where this line intersects the coordinate planes.
     
  4. Sep 15, 2009 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi megr_ftw! :smile:

    I don't understand what you're saying here :confused:

    an intersection is a point, it can't be parallel to a line (or to anything).

    You're asked what is the line through P parallel to the given line. :smile:
     
  5. Sep 15, 2009 #4
    so how do i go about finding that line that is parallel but passes through the certain point?
     
  6. Sep 15, 2009 #5
    So the line in question is parallel to this line:

    [tex]\hat{r}=\left(
    \begin{array}{c}
    1 \\
    2 \\
    3
    \end{array}
    \right) + \left(
    \begin{array}{c}
    3 \\
    4 \\
    5
    \end{array}
    \right)t[/tex]

    Since it passes through the given point as described it must be that the new line is this?

    [tex]

    \hat{s}=\left(
    \begin{array}{c}
    -1 \\
    4 \\
    3
    \end{array}
    \right) + \left(
    \begin{array}{c}
    3 \\
    4 \\
    5
    \end{array}
    \right)t[/tex]

    Intersection of the planes will be found in the instance that:

    [tex] 3t - 1 = 0 [/tex]

    [tex] 4t + 4 = 0 [/tex]

    [tex] 5t + 3 = 0 [/tex]

    For yz-,xz- and xy-planes.

    To find the co-ordinates the values found for t need be plugged into the line s.
     
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