Select all of the following which are possible combinations of ($L_x$, $L_z$) for a 3d state, where $L_\perp = (L_x^2 + L_y^2)^{1/2}$, and $L_x$, $L_y$ and $L_z$ are Cartesian components of the angular momentum vector $\vec{L}$.
(-2, 1.41)$h$
(1.41, -2)$h$
(2, 0)$h$
(0, -2)$h$
(2.45, 0)$h$
What is the total number of different orientations of $\vec{L}$?
5
What is $L_\perp$ for the $m_l = 0$ component? (Enter your answer in terms of $h$.)
2.45$h$
Draw all the possible orientations of $\vec{L}$. (Submit a file with a maximum size of 1 MB.)