Equation of a Plane with Three Points

[nameVoid]

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

 

[tiny-tim]

hi nameVoid!

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

nooo … bc(x-a)+ac(y-b)+ab(z-c) = -2bc

 

[haruspex]

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?

 

[LCKurtz]

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 =?