At the point (1,2,-3) a vectorvmakes 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 directionv.

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

Now I've just got to figure out how I can get the components ofv.

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 ofvmy 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?