Equation tangent with a plane

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



Find the equation of the tangent plane at (2,3,2) to the surface below.
x^2 + y^2 - xyz = 1

The question asks me to do this in two way, one is to view the surface as the graph of a function of two variables z = g(x,y). and the other one is to view the surface as a level surface for a function f(x,y z).

Homework Equations





The Attempt at a Solution



For the first part, I already got an answer of z = (-x+y+5)/3, and so the answer to the second one I assume is x-y+3z-5 = 0. but why is it wrong? am I doing something wrong here?
 

Answers and Replies

  • #2
Dick
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z = (-x+y+5)/3 and x-y+3z-5 = 0 are the same plane. How can one be right and the other one be wrong?
 
  • #3
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That's why I am confused as well... I thought I misunderstand the question for a reason... as one asks to answer it to view the surface as the graph of a func of two variables and the other one as three...
 
  • #4
Dick
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One is probably suggesting you use a cross product and the other to use a gradient to find the normal. But they should both give you the same answer. And they do. Why do you think it's wrong?
 
  • #5
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I don't think it's wrong, I think it's correct, but it's a web assign problem and when I submit the answer above it marks it as wrong. However the z = (-x+y+5)/3 is accepted
 
  • #6
Dick
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That's web assign's problem. Who do you believe? I think you are correct.
 
  • #7
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ok then... hoping for some more inputs
 

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