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Math Help - What's the parametric equation for the line through point ...

  1. #1
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    What's the parametric equation for the line through point ...

    Find the parametric equations for the line through the point p(1,4,8) that is parallel to the plane x+y+z = 8 and perpendicular to the line x = 5+t, y = 1 - t, z = 5t?

    Choices
    1) x = 1 + t. y = a + t, z = 8 - 2t
    2) x = 1 + 6t, y = 4 + 4t, z = 8 + t
    3) x = 1 - 6t, y = 4 + 4t, z = 8 + 2t
    4) x = 1 + 6t, y = 4 + 4t. z = 8 + 2t
    5) x = 1 - 6t, y = 4 + 4t, z = 8 + t

    I thought it was #4, but I'm not sure. I got (6, 4, -6) then I did it.
    Thanks
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  2. #2
    A Plied Mathematician
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    Well, how do you propose to solve it? What steps did you take?
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  3. #3
    MHF Contributor

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    Notice that you are given two vectors that this line must be perpendicular to.
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  4. #4
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    x + y + z = 8 is <1,1,1> which is the natural = n
    then
    x = 5+t, y = 1 - t, z = 5t = <5, -1, 5> = L1
    so then you do the cross product of n and L1
    which I got
    <6,0,-6)
    At this point I am confused. I've already tried answered 2 and 4 which were both wrong. I believe I may be doing something very wrong or be confused as to what to do afterward. Thanks
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