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Math Help - vector help-->equation of planes

  1. #1
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    vector help-->equation of planes

    here's the question:

    determine wheter or not a single plane passes through the following lines:

    L1: [x-1, y-2, z+3]= k[-4, -1, 8] L2: [x, y,z] = [-11, -1, 21]+L[8,2, -16]

    if a plane exists, find its scalar equ'n



    plz help..
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  2. #2
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    The lines obviously are parallel (the direction vectors are scalar multiples), so there is a plane that contains them. There are lots of ways to find the equation of that plane, but if you have technology at hand, the fastest way is probably to solve a system created by the points you can get out of your lines:

    A(1) + B(2) + C(-3) + D = 0 (L1, k=0)

    A(-3) + B(1) + C(5) + D = 0 (L1, k=1)

    A(-11) + B(-1) + C(21) + D = 0 (L2, L=0)

    A(-3) + B(1) + C(5) + D = 0 (L2, L=1)
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  3. #3
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    Quote Originally Posted by sweetbee View Post
    determine wheter or not a single plane passes through the following lines:
    L1: [x-1, y-2, z+3]= k[-4, -1, 8] L2: [x, y,z] = [-11, -1, 21]+L[8,2, -16]
    if a plane exists, find its scalar equ'n
    I can show that the two equations represent the same line.
    Can you?
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