Abs of curl

1. Feb 4, 2014

Jhenrique

Is correct to affirm that:
$$| \nabla \times \vec{f} | = \nabla \times \vec{f} \cdot \hat{n}$$?

I asked thinking in this definition:

http://en.wikipedia.org/wiki/Curl_(mathematics)

Ie, if the affirmation above is correct, so, is correct to express the definition aboce as:
$$\lim_{A \rightarrow 0} \frac{1}{|A|}\oint _{C} \vec{F}\cdot d\vec{r} = |\nabla \times \vec{f} |$$?