Calculate direction vector of azimuth and Elevation in NED I need to calculate the unit direction vector of given azimuth and elevation angles. My target coordinate System is a NED (North east down). 
https://de.wikipedia.org/wiki/Roll-Nick-Gier-Winkel#/media/File:RPY_angles_of_airplanes.png
I found Finding the (unit) direction vector given azimuth and elevation but it is for another coordinate System and i can't reproduce it, because i do not understand this sentence in this post: "I have a right-handed coordinate system with z-up and looking down +y "
Can someone tell me how to get the vector for my coordinate System?
 A: I'm actually not convinced the linked question is answered correctly,
but in any case I think it's simpler to answer this question from
first principles rather than try to adapt another question's answer.

To summarize NED coordinates, the first coordinate axis points due north (N),
the second points due east (E), and the third points straight down (D).
I will label these axes $x$, $y$, and $z$, respectively,
as shown in your figure.
Start with a unit vector pointing due north, which is in the direction
of the $x$-axis:
$$
\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}.
$$
For elevation by an angle $\theta$
(oriented so that positive elevation produces a negative $z$ component),
we rotate this vector to the position
$$
\begin{pmatrix} \cos\theta \\ 0 \\ -\sin\theta \end{pmatrix}.
$$
For azimuth angle $\psi$, we rotate the vector around the $z$
axis through the angle $\psi$ in the direction of rotation
from the $x$ axis toward the $y$ axis.
Viewing the vector componentwise, the $z$ component is unchanged
but the $x$ component is rotated in the $x,y$ plane so that the
vector becomes
$$
\begin{pmatrix} \cos\theta \cos\psi \\
                \cos\theta \sin\psi \\
                -\sin\theta         \end{pmatrix}.
$$
