Adding yaw and pitch of two vectors?

I need to add two unit-length vectors but I don't know what this is called in order to look for it.

After a lot of fussing, it seems that I only get correct results when one of the two vectors has a pitch or yaw of 0. I still haven't been able to picture this in my mind, why doesn't totalling the pitch and yaw work?

[Obli]

Do you want to add the vectors or their angles? I am somewhat confused by the message.

I need to add the angles.

One vector is my camera's orientation and the other is the direction the cursor would project outwards in the frustrum. The cursor vector is relative to the camera's real-world vector, so adding the angles of the two would produce a real-world cursor vector. That's what I'm assuming anyway. It works fine right now if I don't pitch the camera.