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Math Help - Normal Vector Help

  1. #1
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    Normal Vector Help

    Find parametric equations of the line of intersection of the two planes
    -8 x - 2 y + 3 z = 9
    and
    5 x + 4 y + 2 z = -8
    . Assign your direction vector, as a Maple list, to the name DirectionVector.


    ================================================== ======

    This is a repeat question that i cant figure out. If you take the crossproduct o both vectors, that returns you the normal vector which is apraeel correct? The answer i got is [-16,31,-22], but the computer keeps telling me that its not parallel to a correct direction vector for the line. Happy labor day everyone.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The direction vector of the line of intersection of the planes is perpindicular to both planes therefore perpindicular to the normals

    of the 2 planes.

    Also the cross product of the 2 normals is perpindicular to both planes.
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    The direction vector of the line of intersection of the planes is perpindicular to both planes therefore perpindicular to the normals

    of the 2 planes.

    Also the cross product of the 2 normals is perpindicular to both planes.

    Im still confused on how to use that information to find a direction vector that is parallel to the correct direction vector for the line. here is what my computer is telling me:

    "Your Direction vector is not parallel to a correct Direction vector for the line."
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  4. #4
    MHF Contributor Calculus26's Avatar
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    [-16,31,-22] is the correct direction vector

    If you still don't believe what I' saying there is Another way of seeing this verify:

    (-10/11,-19/22,0) and (0,-21/8,5/4) are on the line of intersection

    Compute the vector between these 2 points and you get

    a mutiple of [-16,31,-22] namely 5/88 [-16,31,-22] again verifying

    [-16,31,-22] is the correct direction vector.

    Thnk about what I said: (don't rely always on what the computer says)

    The direction vector of the line of intersection of the planes is perpindicular to both planes therefore perpindicular to the normals

    of the 2 planes.

    Also the cross product of the 2 normals is perpindicular to both planes.

    This will be my last post on this matter
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