# Very quick question about notation of vector fields

Dvsdvs
this is a very quick question. my teacher wants me to prove that
((kq)/(sqroot(x^2+y^2+z^2))) (x,y,z) is conservative. by this does it mean that
F=((kq)/(sqroot(x^2+y^2+z^2)))i+((kq)/(sqroot(x^2+y^2+z^2)))j+((kq)/(sqroot(x^2+y^2+z^2)))k

or does it she mean that
F=((kq)/(sqroot(x^2+y^2+z^2)))Xi+((kq)/(sqroot(x^2+y^2+z^2)))Yj+((kq)/(sqroot(x^2+y^2+z^2)))Zk

Basically I am asking if that (x,y,z) is being distrubuted or its just acting as the (i,j,k) itself Thank you very much
Edit oops, forgot the ^3 power in the denominator. But you guys get the point

Last edited:

Dvsdvs
correct me if I'm wrong but i think it's the second one with the xyz being distributed

Homework Helper
Gold Member
this is a very quick question. my teacher wants me to prove that
((kq)/(sqroot(x^2+y^2+z^2))) (x,y,z) is conservative. by this does it mean that
F=((kq)/(sqroot(x^2+y^2+z^2)))i+((kq)/(sqroot(x^2+y^2+z^2)))j+((kq)/(sqroot(x^2+y^2+z^2)))k

or does it she mean that
F=((kq)/(sqroot(x^2+y^2+z^2)))Xi+((kq)/(sqroot(x^2+y^2+z^2)))Yj+((kq)/(sqroot(x^2+y^2+z^2)))Zk

Basically I am asking if that (x,y,z) is being distrubuted or its just acting as the (i,j,k) itself Thank you very much
Edit oops, forgot the ^3 power in the denominator. But you guys get the point

The second one is correct.

It essentially corresponds to the electrostatic field of a point charge at the origin.