Directional derivative with angle

[-EquinoX-]

That's all the question provides, pi/4

 

[djeitnstine]

This is a conceptual question as it says "of a vector" so that means of any normal vector $$\vec{n}\cdot\vec{T}=0$$ (orthogonality condition)

 

[-EquinoX-]

hmm..are you sure?

 

[Dick]

This is a conceptual question as it says "of a vector" so that means of any normal vector $$\vec{n}\cdot\vec{T}=0$$ (orthogonality condition)

I think I see what djeitnstine is saying. The directional derivative is grad(f).n. You also know an expression for the dot product in terms of the lengths of the vectors and the angle between them, I hope.

 

[HallsofIvy]

Say the question is like this:

Find the directional derivative of f(x,y,z) = xy + z2 at the point(2,2,3) in the direction of a vector making an angle of pi/4 with gradf (2,2,3). Give an exact answer.

Therefore my first step is to find the gradient and I need to something similar to what I've done with this question, however.. how do I find the vector if all I know is pi/4

One major problem with this is that there are an infinite number of vectors "in the direction of a vector making an angle of pi/4 with gradf (2,2,3)". That is NOT a unique direction.

 

[djeitnstine]

hmm..are you sure?

Yes I'm sure, I've done it quite a number of times.