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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!

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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? –  Israel Cohen-Pavon 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. –  Israel Cohen-Pavon Mar 12 '13 at 11:36

1 Answer 1

I'll write this as an answer:

First try roughly sketching the surfaces, to see what's going on. You should immediately realise that the distance is zero, as I gave away in my comment. It is then straightforward algebra to prove that this is true.

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first, thanks. second: if it wasn't zero, how would i solve it? –  Israel Cohen-Pavon Mar 12 '13 at 11:25

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