3
\renewcommand{\vec}[1]{\mathbm{#1}}

Then I write

\[\vec{a}\]

which yields an error:

! Undefined control sequence.
\vec #1->\mathbm 
                 {#1}
l.564 \[\vec{a}
               \]
? 
6

If you're interested in printing boldface mathematics, use \mathbf{...} instead:

\renewcommand{\vec}[1]{\mathbf{#1}}%

Alternatively, you need to use

\usepackage{bm}% http://ctan.org/pkg/bm
...
\renewcommand{\vec}[1]{\bm{#1}}% Bold math

This shows the difference:

Difference between bm and mathbf

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