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Math Help - Quick Question: Planes

  1. #1
    Junior Member Lonehwolf's Avatar
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    Quick Question: Planes

    Two planes A and B have vector equations r.(2i+j-2k)=3 and r.(2i+j-2k)=9. Explain why A and B are parallel and hence find the distance between them.

    Parallel since the perpendicular direction is equal (2i+j-2k) but I have no idea how to calculate the distance
    Meh, too late, no replies. Well, I still don't mind an answer to the question I guess...
    Last edited by Lonehwolf; January 14th 2009 at 04:36 AM.
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by Lonehwolf View Post
    Meh, too late, no replies. Well, I still don't mind an answer to the question I guess...
    For both equations |\vec n| = 3.
    Re-write both equations into Hesse normal form:

    \vec r \cdot (2, 1, -2) -3=0~\implies~\vec r \cdot \dfrac{(2,1, -2)}3 - 1=0

    \vec r \cdot (2, 1, -2) -9=0~\implies~\vec r \cdot \dfrac{(2,1, -2)}3 - 3=0

    The constant summand equals the distance of the origin to the plane. The difference of those distances equals the distance between the planes:

    d_{planes} = 3-1 = 2
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