Express $\left<3x+6y,3x+7y,0\right>$ as the sum of a curl free vector field and a divergence free vector field.

$\left<3x+6y,3x+7y,0\right> =$ + ,
where the first vector in the sum is curl free and the second is divergence free.
(For this problem, enter your vectors with angle-bracket notation: $<a, b, c>$, not in $ijk$-notation.)