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what's the difference between $|\nabla f|$ and $\nabla f$ for example in :

$$\nabla\cdot{\nabla f\over|\nabla f|}$$

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Thank you. I edited the question – user71465 Feb 2 '13 at 12:57
You might want to have a look here, for the different uses of the del operator. – begeistzwerst Feb 2 '13 at 12:59
The vertical bars. – Did Feb 2 '13 at 12:59
up vote 4 down vote accepted

$|\nabla f|$ is the magnitude of the $\nabla f$ vector. The expression $\frac{\nabla f}{|\nabla f|}$ is thus a unit vector.

$\nabla$ (gradient) acts on a scalar to give a vector, and $\nabla\cdot$ (divergence) acts on a vector to give a scalar.

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