Find Unit Vectors for f(x,y) w/ D_uf=0

[Cpt Qwark]

Homework Statement

For f(x,y)=x^2-xy+y^2 and the vector u=i+j.
ii)Find two unit vectors such D_vf=0

Homework Equations

N/A.

The Attempt at a Solution

Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum value of D_uf which was \sqrt{2}.

 

[Fightfish]

The directional derivative is defined as
D_{v}f = \nabla f \cdot \mathbf{v}
Your task is to find two vectors \mathbf{v} such that D_{v}f = 0.

 

[HallsofIvy]

Homework Statement

For f(x,y)=x^2-xy+y^2 and the vector u=i+j.
ii)Find two unit vectors such D_vf=0

This problem doesn't have anything to do with the vector "u". Why is that given? D_vf is the dot product of the gradient, \nabla f, and a unit vector in the same direction as vector v. Since you want that to be 0, you are looking for two unit vectors perpendicular to \nabla f.

2. Homework Equations

N/A.

The Attempt at a Solution

Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum value of D_uf which was \sqrt{2}.

So "u" was used in previous questions?