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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 \[ p(xx_0)+r(yy_0)+s(zz_0) =0\] How?
 one year ago
 one year ago
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 \[ p(xx_0)+r(yy_0)+s(zz_0) =0\] How?
 one year ago
 one year ago

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TuringTestBest ResponseYou've already chosen the best response.0
I would walk you through this personally, but my connection sucks right now, so... http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes.aspx
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.2
think of it as a dot product...
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.2
(x xo), (yyo) etc are the components of any vector in the plane....
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.2
if <p,r,s > dot < any vector in the plane>=0, then <p,r,s> is normal to the plane and defines the surface..
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.2
or the orientation of the surface, rather
 one year ago

henpenBest ResponseYou've already chosen the best response.0
Yes, POMN says similarly. I think I've got the intuition, thanks both.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.2
oh, Paul's online math notes... never mind:)
 one year ago
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