The trio were caught by North Yorkshire Police during Operation Tramline, which is returning this month and will see officers patrolling the county's main routes in a HGV cab, loaned to the force by Highways England.
The elevated ride height gives them a better view of all drivers to help police detect mobile phone use and other dangerous behaviour.
North Yorkshire Police Traffic Constable Mark Patterson said: “In my time as a traffic officer, I’ve seen crashes where people have died or suffered life-changing injuries just because a motorist got distracted.
“All drivers on our roads know using a mobile phone while driving is wrong. But nobody thinks they’ll be the driver that causes one of those incidents.
“Catching those offences as they happen, then using enforcement and education is one way we can make our roads safer for everyone.
“Using Highways England’s HGV cab during Op Tramline is an excellent way to do that, as it gives us an unparalleled vantage point.”
Several other roads policing units also take part in the operation.
If officers in the lorry see an offence taking place, it is recorded by the passenger. Marked units then pull the vehicle over so the driver can be dealt with immediately.
North Yorkshire Police ran the same operation last spring. While they found most road users were “overwhelmingly responsible”, they detected a number of offences including the tractor driver driving on the motorway using his phone; the man who took both hands off the wheel to use his phone; and the lorry driver who rolled a cigarette.
Officers also discovered a European-registered HGV with extensive collision damage which the driver was intending on driving to Dover and a disqualified driver driving an overweight van and trailer while using his mobile phone.
The drivers received fixed penalty notices, which typically include a fine and points on their licence.