VC3.13

From Exampleproblems

$a\cdot\nabla=[(x+3y)i+(y-3z)j+(x-2z)k]\cdot[i\frac{\partial}{\partial x}+j\frac{\partial}{\partial y}+k\frac{\partial}{\partial z}]\,$

= $(x+3y)\frac{\partial}{\partial x}+(y-3z)\frac{\partial}{\partial y}+(x-2z)\frac{\partial}{\partial z}\,$

Now, $(a\cdot\nabla)a=[(x+3y)\frac{\partial}{\partial x}+(y-3z)\frac{\partial}{\partial y}+(x-2z)\frac{\partial}{\partial z}][(x+3y)i+(y-3z)j+(x-2z)k]\,$

= $(x+3y)\frac{\partial}{\partial x}[(x+3y)i+(y-3z)j+(x-2z)k]+(y-3z)\frac{\partial}{\partial y}[(x+3y)i+(y-3z)j+(x-2z)k]+\frac{\partial}{\partial z}[(x+3y)i+(y-3z)j+(x-2z)k]\,$