Tangent Plane Equation for Surface x^2 + y^2 - xyz = 1 at Point (2,3,2)

[-EquinoX-]

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?

 

[Dick]

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?

 

[-EquinoX-]

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...

 

[Dick]

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?

 

[-EquinoX-]

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

 

[Dick]

That's web assign's problem. Who do you believe? I think you are correct.

 

[-EquinoX-]

ok then... hoping for some more inputs