Rate of change f(x,y,z) in direction v

At the point (1,2,-3) a vector **v **makes an angle of pi/3 radians with the gradient of the function,

$\displaystyle f(x,y,z) = x^2yz - 3xy^3$

Find the rate of change of f(x,y,z) in direction **v**.

Okay so if I can find the components of the vector **v** then I simply have to dot the gradient of the function evaluated at the point (1,2,-3) with a unit vector in the direction of **v**.

Now I've just got to figure out how I can get the components of **v**.

The dot product would give me on equation, the cross product another, but where do I get the last equation?

I guess because I specified it has to be a unit vector in the direction of **v** my last equation would be that the magnitude of the vector must be equal to 1.

Is this the only way to solve this problem?

**EDIT: I'm stuck with this one, cross product didn't work out so well. Any ideas?**