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## Homework Statement

Suppose f is a smooth function of x and y, and at the point (1,1), [itex]\partial[/itex]f/[itex]\partial[/itex]x = 1, [itex]\partial[/itex]f/[itex]\partial[/itex]y = -1.

Find the unit vector

**u**such that D

_{u}f(1,1) = 0

## Homework Equations

D

_{u}f(1,1) = [itex]\nabla[/itex]f(1,1) *

**u**= 0

## The Attempt at a Solution

My answer was merely

**u**= k, which is the unit vector k of course (I don't know how to put the symbol on this. Work it out, I don't see how it is wrong. I will tell you why they said that I was wrong, and I will give my argument after an answer or two.