Thread: scalar/vector field question

hey guys, i've been asked to consider the scalar field:

f(x,y,z) = xy + xz + yz

after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?

Originally Posted by ben08

hey guys, i've been asked to consider the scalar field:

f(x,y,z) = xy + xz + yz

after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?

Yes. I agree that it sounds a bit odd to use the word field here. I suppose the idea is that it is a constant vector field, taking the value [2,-1,1] at every point (including in particular the point (1,1,1)).

Originally Posted by ben08

hey guys, i've been asked to consider the scalar field:

f(x,y,z) = xy + xz + yz

after finding grad f, i am asked to find the directional derivative of f at the point P (1,1,1) along the vector field u = [2,-1,1].

the bit that has confused me is finding the directional derivative of f along the vector FIELD u... do i just calculate the dot product of grad f and the unit vector of u?

Yes.

RonL