Calculating Velocity from Speed, X,Y Bearing, and Z Bearing

Question

I'm not entirely sure how to go about it, but I have a data structure that gives me

Speed
Bearing - Direction in the XY Plane 
Z-Bearing - Direction in the Z Plane

How can I combine these into a 3 dimensional velocity vector?

I assume it's something like

Xvel = cos(bearing) * speed * cos(Z-Bearing)
Yvel = sin(bearing) * speed * cos(Z-Bearing)
Zvel = sin(Z-Bearing)

Buut I'm not entirely sure I'm correct.

Answer 1

You basically have it correct, presuming the interpretation of $Z$-plane (which doesn't quite make sense) works.

You do want Zvel = speed * sin(Z-Bearing) though.

See Spherical coordinate systems, where the usual convention is that $Z$-bearing $0$ is directly in the $Z$-direction, so flip mentions of sin and cos(Z-bearing).