Equation of a Plane with Three Points

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Homework Help Overview

The discussion revolves around finding the equation of a plane defined by three points in three-dimensional space, specifically the points (a,0,0), (0,b,0), and (0,0,c). Participants are exploring the formulation of the plane's equation and the properties of vectors associated with it.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the derivation of the plane's equation using normal vectors and point coordinates. There are attempts to clarify the correct formulation of the equation, with some questioning the validity of specific terms and constants involved. Others are exploring what it means for a point to lie on the plane and how to derive vectors parallel to it.

Discussion Status

The discussion is ongoing, with various interpretations of the plane's equation being explored. Some participants have offered alternative formulations and questioned the assumptions made about the points and vectors involved. There is no explicit consensus on the correct equation at this stage.

Contextual Notes

Participants are navigating potential discrepancies between their calculations and those presented in a textbook. There are also discussions about the implications of certain points not lying on the plane and what that means for the equation being derived.

nameVoid
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Equation of plane containing points (a,0,0) (0,b,0) (0,0,c)

Vectors
<-a,b,0> <-a,0,c>
Normal vector
<bc,ac,ab>

Plane
Bc(x-a)+ac(y-b)+ab(z-c)=
Bcx+acy+Abz=3abc
Book is showing = abc
 
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hi nameVoid! :smile:
nameVoid said:
Bc(x-a)+ac(y-b)+ab(z-c)=

nooo … bc(x-a)+ac(y-b)+ab(z-c) = -2bc :wink:
 
nameVoid said:
Equation of plane containing points (a,0,0) (0,b,0) (0,0,c)
Normal vector
<bc,ac,ab>
If the point <x, y, z> lies in the plane, what do you have to subtract to get a vector parallel to the plane?
 
nameVoid said:
Equation of plane containing points (a,0,0) (0,b,0) (0,0,c)

Vectors
<-a,b,0> <-a,0,c>
Normal vector
<bc,ac,ab>

Plane
Bc(x-a)+ac(y-b)+ab(z-c)=

(a,b,c) is not a point on the plane, but (a,0,0) is. And what should the right side =?
 

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