Plane Equations

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  • #1
PFuser1232
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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.
 

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  • #2
jbriggs444
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You must decide what "same side of the origin" means for non-parallel planes.
 
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  • #3
PFuser1232
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You must decide what "same side of the origin" means for non-parallel planes.

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?
 
  • #4
jbriggs444
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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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