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henpen
 2 years 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?
henpen
 2 years 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?

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

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

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

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

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

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

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