The accident happened shortly after 11 a.m. Wednesday near Alderman Road south of the Gray's Creek community, when troopers believe the car pulled in front of the truck.
Troopers said the truck's driver, Winford King, was unable to stop in time and collided with the car, causing it to run off the roadway.
"This is probably as bad as it can get when you enter the path of a tractor-trailer," said Sgt. Joel Siles, with the Highway Patrol.
The driver and passengers in the car, Amber Currier, Jackier Larrison and 12-year-old James Larrison, died.
At one point, at least 10 state trooper vehicles were at the scene.
While authorities have closed the southbound lanes of Highway 87, there were no reports of traffic congestion.
The Highway Patrol said it will not file charges against King.
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