Find a parametrization of the line through the origin whose projection on the $xy$-plane is a line of slope 3
and on the $yz$-plane is a line of slope 6 $($i.e., $\Delta z / \Delta y = 6)$.
Scale your answer so that the smallest coefficient is 1.

$\mathbf r (t) = \langle$$t,$$t,$$t \rangle$