Unit vector perpendicular to the level curve at point

[Bestphysics112]

Homework Statement

Find the unit vector perpendicular to the level curve of f(x,y) = x²y-10xy-9y² at (2,-1)

Homework Equations

Gradient

The Attempt at a Solution

I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing something?

 

[Orodruin]

Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized?

Yes. Is that a problem?

 

[Bestphysics112]

Yes. Is that a problem?

No problem at all. I just wasn't sure what a level curve was.

 

[Orodruin]

A level curve of a function is the curve such that the function takes a fixed value. For example, the level curves of f=x^2+y^2 are circles.

 

[Bestphysics112]

A level curve of a function is the curve such that the function takes a fixed value. For example, the level curves of f=x^2+y^2 are circles.

Oh that makes much more sense. Thank you.