I kinda understand the reasoning behind it: You're finding the gradient in all x, y, and z directions so they are all going to be perpendicular to each other. Thus the product of the gradients will equal minus one.

But I can't understand the proof. Why have they let dz = 0??

Any help appreciated

(Here's the proof I'm talking about http://en.wikipedia.org/wiki/Triple_product_rule)

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