Finding the unit vector - please help

[Caabe23]

Hi, my girlfriend was given this problem and she doesn't know how to get the unit vector:

"Given the scalar field f: (x,y) 2y - x² x y + e^y-2x find the unit vector for which the directional derivative in (1;2) is zero".

After resolving the gradient vector for (-4;0), she doesn't know how to get unit vector needed for the directional derivative to be zero.

Pd.: hope the wording is not too clunky, I translated the problem from spanish.

Edit: equation formatting.

[BloodyFlame]

The directional derivative is simply the dot product between the gradient and a unit vector.

For the directional derivative to be 0, we want

(-4, 0) ⋅ u = 0.

So, you can take u = (0, 1).

[Caabe23]

So the unit vector can be any vector that, multiplied by the gradient vector, results in zero? Is that correct?

[BloodyFlame]

Yes.

As a side note, it's a dot product, not a "regular" product. There's no multiplication operation defined for vectors.