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It is given that at the point \[ [x_0,y_0,z_0] \] the normal vector to the plane is \[ n= [p,r,s] \]. You can deduce from this that the equation of the plane is \[ p(x-x_0)+r(y-y_0)+s(z-z_0) =0\] How?

Mathematics
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I would walk you through this personally, but my connection sucks right now, so... http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes.aspx
think of it as a dot product...
(x -xo), (y-yo) etc are the components of any vector in the plane....

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Other answers:

if dot < any vector in the plane>=0, then is normal to the plane and defines the surface..
or the orientation of the surface, rather
Yes, POMN says similarly. I think I've got the intuition, thanks both.
what's POMN?
oh, Paul's online math notes... never mind:)

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