Why Does the Divergence of r-hat Over r-squared Equal Zero?

[manimaran1605]

Homework Statement

How divergence of r (cap)/ |r|^2 is equal to zero?

Homework Equations

r(cap)= x(cap)+y(cap)+z(cap)

|r|^2 as x^2+y^2+z^2

The Attempt at a Solution

I tried the problem and end up with with a different solution I took r(cap)= x(cap)+y(cap)+z(cap)
|r|^2 as x^2+y^2+z^2. Tell me where i went wrong?

where r(cap) is unit vector of r vector
|r|^2 is the square of modulus of r

 

[Quesadilla]

Could you please provide the calculation that lead you to the wrong answer? It is hard to pinpoint where you went wrong otherwise.

 

[vela]

You didn't differentiate correctly. Show your work.

 

[manimaran1605]

Here's my attempt to the problem

 

[Quesadilla]

Well $\mathbf{\hat r} = \mathbf{\hat x} + \mathbf{\hat y} + \mathbf{\hat z}$ seems false. You have $\mathbf{r} = (x,y,z)$. Work from there.