# Math Help - Vector Proof

1. ## Vector Proof

If a and b are arbitrary scalar fields, show that

del.[del(a)xdel(b)] = 0.

Is this anything to do with perpendicular vectors as I remember if two vectors are indeed perp., then the dot product of both of them equals 0. Or is something totally different here?

del = operator which looks like an upside triangle

2. The del operator is defined as $\nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}$.
If each of a & b is a scalar field then $\nabla a = a_x i + a_y j + a_z k\quad \& \quad \nabla b = b_x i + b_y j + b_z k$.
$\nabla \cdot \left( {\nabla a \times \nabla b} \right) = \nabla b \cdot \left( {\nabla \times \nabla a} \right) - \nabla a \cdot \left( {\nabla \times \nabla b} \right)$

3. Will that suffice in answering the question? Or do I need to go further?

4. That should suffice I think...