2.4Ghz radio frequency has a a wave length of 4.92 inches. Normal 'omni directional' antenna (like one used in Broadcast Radios Receiver,Walkie Talkies etc , AND our Tx/Rx), are usually of the length of 1/4 wave length. That amounts to 1.24 inch long antenna for our 2.4Ghz radios.
the Antenna we get in our 2.4G Rx are antenna + Coax feed wire combined (like the flat cable from your TV to roof top Yagi Antenna for Doordarshan reception). When you remove the outer shield of the coax wire (acting as ground) the exposed 'core' becomes the antenna. The extra length in the feed wire is to let you route the 'antenna' part to a suitable location where you have clear reception. My Futaba 6004 2.4g Nano Rx has just an inch antenna, sans the feeder.
Now two antennas. Take your FM radio, extend the telescopic antenna vertically and tune to a fading station so that you barely listen the reception. Now turn the antenna so that it is parallel to ground instead vertical - you loose the signal completely. The two (mutually perpendicular antenna ) in full range Rx are to assist reception in when plane is in different vertical/Horizontal orientation while in flight.
Futaba and also Sanwa (I believe, owners pardon me if wrong) only uses passive duality i,e they have only one receiver pre-amp section and two redundant antennas connected to them. Others like JR/Spectrum have two separate Receiver pre-amps having dedicated orthogonal antennas
Question: Why not 3 antennas to have true 3-Dimensional coverage ?