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Plane Equations

  1. Dec 27, 2014 #1
    According to my book, if we write the equation of a plane as:

    ##ax + by + cz = d##

    And two planes have values of ##d## with the same sign, they are on the same side of the origin. If they have values of ##d## with different signs, they are on opposite sides of the origin.

    I'm confused as to whether this applies strictly to two parallel planes, or any pair of planes.
  2. jcsd
  3. Dec 27, 2014 #2


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    You must decide what "same side of the origin" means for non-parallel planes.
  4. Dec 27, 2014 #3
    What about parallel planes? If both sides of the plane equation (cartesian form) are multiplied by -1, the position of the plane is unaltered, right?
  5. Dec 28, 2014 #4


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    Right. In order to make the "parallel plane" version work, you need for a, b and c to either remain constant or at least to remain proportional and not change signs.
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