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,
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?