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?