Let r=(x,y,z). Find ∇r(hat).
r(hat)= (x,y,z)/sqrt (x^2+y^2+z^2)
∇f=df/dx x + df/dy y...
The Attempt at a Solution
Okay I'm having a complete brain freeze at the moment. I know the denominator is a magnitude but am I still supposed to use the quotient rule here? For the x component of ∇r(hat) we get:
x (sqrt(a) * 1 - x^2 /sqrt(a))/a where a= x^2+y^2+z^2 correct?
Also another stupid question but is the x-component of r(hat) (x,0,0)/sqrt(a) or just x/sqrt(a)?
Would this mean that ∇dot r is a vector while ∇r is a scalar?
r=xi + yj + zk
∇r= (i, j, k) = 3?
My mind is so confused right now...