1. May 22, 2015

### Cpt Qwark

1. The problem statement, all variables and given/known data
For $$f(x,y)=x^2-xy+y^2$$ and the vector $$u=i+j$$.
ii)Find two unit vectors such $$D_vf=0$$

2. Relevant equations
N/A.

3. 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 $$\sqrt{2}$$.

2. May 22, 2015

### 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 $D_{v}f = 0$.

3. May 22, 2015

### HallsofIvy

Staff Emeritus
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 $\nabla f$.

So "u" was used in previous questions?