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Math Help - Finding a parametric equation to a line

  1. #1
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    Finding a parametric equation to a line

    How would you find a parametric equation for a line passing through a point and perpendicular to a line passing through two other points?

    Here is an example given to me, "Find parametric equations of the line passing through (3, -1, 3) and perpendicular to the line passing through (3, -2, 4) and (0, 3, 5)."

    I have been reading around and I've only found information about how to find an equation to a plane but not a line. How would you approach this question? Any help would be appreciated! Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by capitol View Post
    How would you find a parametric equation for a line passing through a point and perpendicular to a line passing through two other points?

    Here is an example given to me, "Find parametric equations of the line passing through (3, -1, 3) and perpendicular to the line passing through (3, -2, 4) and (0, 3, 5)."

    I have been reading around and I've only found information about how to find an equation to a plane but not a line. How would you approach this question? Any help would be appreciated! Thanks!
    First find the parametric equation of the line passing through (3,-2,4) and (0,3,5).

    The equation of the line would be x=3-3t, y=-2+5t z=4+t (I leave it for you to verify this).

    Now, \mathbf{n}=\left<-3,5,1\right>. The line perpendicular to this will have a vector that is perpendicular to \mathbf{n}. Thus, you need to find an \mathbf{m} such that \mathbf{m}\cdot\mathbf{n}=0. Note that \mathbf{m} is not unique!

    So we can say, for example, \mathbf{m}=\left<5,3,0\right>.

    Thus, the equation of our new line will be x=3+5t, y=-1+3t, z=3

    Does this make sense?
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