Thread: Vector Fields...

if f(x,y,z)= x^2+y^2-z

let F be the vector field defined by F=▽f. Calculate ▽. F (scalar product) and ▽X F (cross product)

Not all that sure about where F and ▽have come from, i have done scalar and cross products before but don't really know where to start on this, any help would be much appreciated.

Originally Posted by Ash_underpar

if f(x,y,z)= x^2+y^2-z

let F be the vector field defined by F=▽f. Calculate ▽. F (scalar product) and ▽X F (cross product)

Not all that sure about where F and ▽have come from, i have done scalar and cross products before but don't really know where to start on this, any help would be much appreciated.

take and

note that the dot product gives you and the cross-product gives you

so if ▽= (2x+2y-1) this is multipied by f to get F? which is (2x+2y-1)(x^2+y^2-z)... i'm confused! whats the difference between d/dx and df/dx???

Originally Posted by Ash_underpar

so if ▽= (2x+2y-1) this is multipied by f to get F? which is (2x+2y-1)(x^2+y^2-z)... i'm confused! whats the difference between d/dx and df/dx???

no, is exactly what i told you it was. it doesn't change. it is notation (conventionally) defined as i have it

just write it out as you have it and you will "see" it

by itself makes no sense. this is why i said it is a convention. means the partial derivative of f with respect to x