By Larry Celona and Tamar Lapin

The private plane that crashed near the Hamptonscosting three people their lives, fell out of the sky and into the Atlantic because it’s wing broke off mid-flight, according to a National Transportation Safety Board report.

A witness near Westhampton Beach said they heard a “pop” and saw two large pieces of the seven-seat, twin-engine Piper PA-34 fall from the sky Oct. 13, according to the preliminary accident report obtained by The Post.

The plane, which was last reported to be at above 15,700 ft., did a figure eight turn and began to plummet and did a “nosedive” into the ocean about a mile off Quogue, according to the report.

The aircraft’s carcass was found in 20 feet of water on the ocean floor and a part of its right wing was recovered floating above it about a half mile offshore, the report said.

Owner Raj Persaud, 41, was getting a lesson from a still-unidentified flight instructor and flying from Danbury, Conn. to Charleston, SC, the day of the crash. Both men and a Georgia special education teacher named Jennifer Landrum who was also on board were killed.