How to find ∇||r||, r=xi +yj +zk
My first step:
||r||^2 = r‧r
then don't know how to continue.
Hint: Note that in R^3, r.r = x^2 + y^2 + z^2. With grad = (d/dx,d/dy,d/dz) you need to apply each differential operator to ||r|| to get the answer. (Think about differentiating SQRT(x^2 + y^2 + z^2) with respect to each variable).
You can, but you have to define the mapping.
It may not seem intuitive but all that is happening is that you are dealing with a multi-variable situation that is mapping things between elements of a vector.
With the grad operator you have a vector definition (d/dx,d/dy,d/dz) and you are simply mapping things to different elements of a vector.
The general derivative operator for a multi-variable scenario is just a matrix of derivatives which also happens to be a linear object.
I've asked my classmate and she said the professor will send us the solution tomorrow. haha.
Thank you chiro.
Sorry for wasting your time!!
I think suffix notation is my enemy!!
I lack mathematics intuition and inspiration, but I will work hard!