Find the grad (vector calculus)

[sara_87]

Homework Statement

show that
grad(r.$$\hat{k}$$/r^3) = [r^2$$\hat{k}$$-3(r.$$\hat{k}$$)r]/r^5

Homework Equations

The Attempt at a Solution

I know that r=xi+yj+zk
and i know how to calculate the grad from the formula but, what is r.$$\hat{k}$$ ?
thank you

 

[Dick]

r.k=z. So you can just show it directly by showing both sides are equal. But actually that formula holds for any constant vector 'k'. If f is a scalar function (like r.k) and g is a scalar function (like r^3), grad(f/g)=grad(f)/g-f*grad(g)/g^2. That's what the two different terms on the right side are.