How Do I Convert Angles into Velocities? - Math Problem Help

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Hi PF,

I would really appreciate it if you can help me through this math problem.

I have 3 angles: x, y, and z. I need to convert them into x,y,z velocities (say 5 m/s) in that direction. I have no idea where to even start. Did a lot of searching to no avail :(
 
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