FAA Order 7110.65—the ATC handbook—lays out the vectoring toolbox in section 5-6-2. Let’s roll with the basics: “FLY HEADING (degrees).” The controller wants you to turn to the assigned heading, but which direction should you turn? The Pilot/Controller Glossary’s Fly Heading entry says, “The pilot is expected to turn in the shorter direction to the heading unless otherwise instructed by ATC.” If you’re heading 089, and ATC says “Fly heading 270”, you’ll make your turn to the left. If there’s ever any ambiguity—for instance, if you’re flying 090 degrees and ATC wants a 270-degree heading—verify the direction with the controller.
If ATC indeed needs the turn in a certain direction, they’ll employ the second tool: “TURN LEFT/RIGHT HEADING (degrees).” Let’s say you’re heading 089 degrees again and need a westbound turn, but off your left wing there’s an obstacle or traffic. “Turn right heading 270” ensures you make that turn in a safe direction. If the direction is truly critical or the turn direction is counterintuitive, controllers may add extra emphasis, such as, “Turn right—again, turn right—heading 270.”