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Math Help - planes in space

  1. #1
    Junior Member
    Joined
    Jan 2009
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    71

    planes in space

    could someone help me understand this? i have no idea how to answer it. the question is:
    how can you tell when two places A1x +B1y +C1z=D1 and A2x+B2y+C2z=D2 are parallel? perpindicular? (the 1's and 2's are sub 1 and sub 2, i just don't know how to type that. if it makes any difference...)
    if anyone could give me some help to clarify this it would be much appreciated. thanks.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
    Posts
    1,458
    Hi

    One perpendicular vector to the first plane has coordinates \left(A_1;B_1;C_1\right)

    One perpendicular vector to the second plane has coordinates \left(A_2;B_2;C_2\right)

    The two planes are parallel when the two perpendicular vectors are collinear
    In other words there exists k such that
    A_1 = k A_2
    B_1 = k B_2
    C_1 = k C_2

    By the way they are equal when also D_1 = k D_2

    The two planes are perpendicular when the two perpendicular vectors are perpendicular
    In other words when their dot product is equal to 0
    A_1 \times A_2 + B_1 \times B_2 + C_1 \times C_2 = 0
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