# Significance of a plane equation

• quietrain
In summary, the equation x + y + z = 6 represents a plane with a normal vector of 1, 1, 1. The number 6 on the right hand side of the equation indicates that any point P whose coordinates add up to 6 will lie on the plane. This means that any point (x, y, z) where x + y + z = 6 will be on the plane, while points where x + y + z ≠ 6 will not be on the plane. This also means that the plane extends infinitely in all directions, making it possible for points with seemingly strange coordinates, such as (-50, 0, 56), to still be on the plane. However, it is

#### 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!

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

oh i see thank you

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.

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

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".

oh i see thanks everyone!