A helicopter does have two propellers: one to get the helicopter in the air and the other one to counteract the torque produced by the first propeller so the helicopter doesn't start to spin. Why aren't the two propellers in the same plane? The bigger propeller does have angular momentum pointing in the positive z-direction, the smaller propeller has angular momentum pointing in the direction of the positive y-axis (if the helicopter is situated at the origin). Isn't angular momentum conserved in every component of the (pseudo)-vector that is representing it? What am I overlooking?
Let's start with the helicopter just having the main propeller. If it had just one, the device would start rotating around xy plane's vertical axis due to conservation of angular momentum. A smaller tail rotor is placed in the helicopter (which rotates around an horizontal axis), to prevent helicopter from spinning.
The Both main and tail rotor generate torque due to frictional force
Why are not the two propellers in the same plane? Actually, you could construct it. It will work if you are able to counteract the torque generated by the main helix. That aim can be claimed if both propellers spin in opposite directions.