# Find the grad (vector calculus)

1. Dec 7, 2008

### sara_87

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Dec 7, 2008

### 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.