A drone is navigating a 3D wind field where the air density is given by $\rho(x,y,z) = 100 - x^2 - 2y^2 - 3z^2$. The drone is currently at the point $P(2, 1, 1)$. To maintain its current density, it must move in a direction tangent to the level surface of $\rho$. Among all such directions, find the unit vector $\mathbf{u}$ that maximizes the drone's rate of altitude gain (the $z$-component of its motion).