Significance of a plane equation

[quietrain]

lets say i have a plane equation x + y + z =6

then i know the normal vector is 1 ,1,1 right?

but what does the 6 tells me on the RHS of the equation?

since it is essentially ()x + ()y + ()z, where () is any point on the plane

1)does it mean that i can fit anything into the () as long as i get the total to 6?

like for example 1, 4, 1 gives me 6 too

2)does it then mean that any points i throw in as long as it satisfies 6 will be guaranteed to be a point on that plane?

thanks!

 

[abhishek ghos]

============2)

 

[quietrain]

oh i see thank you

 

[Mark44]

1 and 2 seem to be saying the same thing. For any point P whose coordinates are (x, y, z), if the sum of the coordinates is 6, P is a point on the plane. If the sum of the coordinates is not 6, P is not on the plane.

 

[quietrain]

so i can have (-50 , 0 , 56) as a point on that plane? seems weird :S

 

[HallsofIvy]

Why? The plane extends infinitely in all directions. Its intersection with the plane y= 0 is the line x= t, y= 0, z= 6-t, which extends infinitely.

By the way, "()x + ()y + ()z, where () is any point on the plane" plane makes no sense. It looks like you are saying the coefficients can be any numbers but that is not true. It would make more sense to say "()+ ()+ ()= 6".

 

[quietrain]

oh i see thanks everyone!