Driver Robert Reed, 75, rear seat passenger Natalie Simpson, 18, and her 14-month-old daughter, Destiny Reed, who was in the back seat died at the scene of the crash in County Durham yesterday afternoon.
Mr Reed's 74-year-old wife Margaret, who was a front seat passenger of the Renault Megane Scenic, was taken by helicopter to the James Cook University Hospital in Middlesbrough, where she is said to be in a critical condition.
The driver of the Volvo truck, a 42-year-old man, from Hetton-Le-Hole, was treated for whiplash and arrested on suspicion of causing death by dangerous driving, police said.
He is currently in police custody and will be questioned today, police said.
Friends of Ms Simpson, who was the partner of Mr and Mrs Reed's grandson, have taken to Twitter to pay tribute to the 'bubbly' mother and her 'beautiful baby girl'.
One wrote: ‘You were bubbly, smiley always good to get a long with, always were a good friend and always there when I was feeling down.’
The friend wrote that Destiny was ‘such a beautiful baby girl, with such lovely parents.’
Scroll down for video
Carnage: Three members of the same family, including a on-year-old baby, who were in this car, were killed following a head-on collision with a lorry today
Wreckage: The Renault Scenic people carrier carrying four members of the same family - three of whom were killed - was devastated by the impact on the B1404
Friends have set up a tribute page on Facebook called ‘RIP Natalie Simpson and her baby girl you will never be forgotten’.
The incidents happened near Sharpley Golf Club on the B1404 between Houghton-le-Spring and Seaham at around 12.20pm, Durham Police said.
The force of the crash sent the lorry through a fence and on to the 15th fairway, 250 metres from the impact.
‘The road has been closed to traffic and is expected to be so for several hours,’ he added.
Simon Weightman, a farmer who diversified to build Sharpley Golf Club, said: ‘I suddenly saw a lorry in the middle of the fairway.
Horror: The driver of the Volvo truck has been arrested on suspicion of causing death by dangerous driving following the fatal crash on the B1404 near Houghton Le-Spring from Seaham in County Durham this afternoon‘Then I saw a person get out and collapse on the ground.
‘Some golfers playing that hole turned out to be detectives and they were very quickly on the scene of the crash.
‘The bang was so loud I thought it must have been a head-on collision.
‘The lorry's fuel tank was ruptured as if the lorry had gone over the car.
‘I got a quick glimpse of the car but it was very traumatic to see it.
‘Golfers who saw it came off the course. They could clearly see it was awful.’
Mr Weightman said the crash happened on a 60mph stretch of road, close to the bottom end of the course.
He said: ‘After the collision it had gone through the old hedge, through the new one, up an embankment, over the top of some five-year-old trees and into the fairway.
Trail of destruction: The lorry smashed through a fence and hedgerow and over an earth bank following the fatal collision today
The force of the collision was so violent the lorry carried on hundreds of yards off the road on to Sharpley Golf Club, County Durham
‘The front of the lorry was damaged and the tyres were ruptured.
‘The driver of the lorry only seemed to get 30 yards from the vehicle and then collapsed.’
Mr Weightman said there had been several bad crashes on the stretch of road since he moved to the farm in 1989 and it was the third time the air ambulance has attended.
‘There has been a lot of vehicles go through the hedge and that has generally been associated with speed.
‘We really should have a 50mph limit here,’ he said.
A spokesman for the Great North Air Ambulance confirmed they were called to the scene at 12.25pm.
He said a female casualty was taken to James Cook University Hospital with serious injuries.