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An infantry type unit may attack a vehicle in the same hex using the vehicle's back armour, right?
Correct. This is covered under "Facing" on p.30.
How about the vehicle if it's a unit which may only attack units "in front of it", may this vehicle attack the infantry type unit in its hex?
This is straight from the rules:
A hex is “in front of” a unit if a line from the center of that hex to the center of the unit’s hex goes through one of the front three sides of the unit’s hex or through one of the front two corners of the hex.
A hex is “behind” a unit if the line goes through one of the three rear sides of the hex or through one of the two rear corners.
If the hex is directly to the left or right of the unit’s hex, then that hex is neither in front of nor behind the unit. The hex that the unit is in is also neither in front of nor behind the unit.
Therefore, if a vehicle can only attack "Units" "in front of" it, then it may not attack units in the same hex. Note that some vehicles state they may only attack "vehicles" "in front of" them which would allow them to attack other types of units (i.e. soldiers) in the same hex as long as they have an anti-personnel value.