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henpen
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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?
 2 years ago
 2 years ago
henpen Group Title
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?
 2 years ago
 2 years ago

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TuringTest Group TitleBest 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
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
think of it as a dot product...
 2 years ago

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

Algebraic! Group TitleBest 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..
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
or the orientation of the surface, rather
 2 years ago

henpen Group TitleBest ResponseYou've already chosen the best response.0
Yes, POMN says similarly. I think I've got the intuition, thanks both.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.2
what's POMN?
 2 years ago

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