The victims were returning home in Babupur Saraya from Jagdishpur after some treatment.
They were riding pillion while one Hasan Ali was driving the bike, they said.
The victims have been identified as Mohammad Kaif (11), Mosima (65) and Rasidulnisha (35). They died on spot.
Hasan Ali was severely injured and has been admitted to hospital.
The truck driver managed to flee the spot, but his vehicle has been taken into custody, police said.