Show That Vector Squared is Equal to 12r

[Nat3]

Homework Statement

$$\vec r = <x, y, z>, r = \left |\vec r \right |$$

Show that $$\nabla ^2 r^3 = 12r$$

Homework Equations

I don't understand how a vector can be squared. What does $$\nabla ^2$$ mean?

 

[Dick]

del^2 is d^2/dx^2+d^2/dy^2+d^2/dz^2. It's the sum of the second derivatives. It's the laplacian.

 

[eshaw]

Like Dick said nabla squared is called the laplacian. Don't forget that r=sqrt{x^2+y^2+z^2}, This problem is going to be a lot of work.

 

[Pengwuino]

Do you know index notation? This is a 3-liner if you know it. Although come to think of it if you haven't seen the Laplacian, then you probably don't.