# Find the distance between a surface and a plane

Hi guys I have another question thats giving me a hard time, can someone please help me out with it ?

I need to find the distance between a surface and a plane. I know that it has to be something with lagrange multipliers but i dont really know how to define the functions for it.

the surface is $$\{(x,y,z) | x^2+y^2=z \}$$ and the plane $$-2x-2y+z=7$$

thank you very much!

-
Are you sure those equations are right? Because as they stand, the distance is zero... – Rhys Mar 12 '13 at 11:09
yes I'm sure. how did you solve it? – Srol Mar 12 '13 at 11:15
Just to clarify, you understand that the distance will be zero if the surface and plane intersect anywhere, right? – Sparr Mar 12 '13 at 11:22
yes. but i don't understand how to know if the distance is 0 if i couldn't see it in the drawing. – Srol Mar 12 '13 at 11:36