# Significance of a plane equation

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

Mark44
Mentor
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

HallsofIvy