Consider the following vector in a cartesian rectangular coordinate, $x_1,x_2$ system:

vec$(a)=a_1$hat$()+a_2$hat$(),$ where $a_1=2\mathrm{.}000,a_2=3\mathrm{.}000$ and hat$(),j$ are the unit vectors.

Determine the magnitude of the vector.

$3\mathrm{.}606$

$5\mathrm{.}000$

$7\mathrm{.}211$

$10\mathrm{.}198$