Can a 10-2 wire be connected to a 10-3 recepticle for a dryer?

No, the dryer needs 120 volts supplied by the neutral third wire, along with the 240 volts for the dryer element. One of the two 240 volt supply conductors is used with the neutral to supply 120 volts to the controls and the drum motor. That is why a three wire cable is needed.