乘 is more formal than 坐 for 'to ride'. In everyday speech 坐飞机 is more common than 乘飞机, but both are correct. 乘 also covers grabbing an opening: 乘机 can mean both 'to take a plane' and 'to seize the chance' depending on context.
mistakes
乘 has a second reading 乘 used in classical/literary words: 千乘之国 (a state with a thousand war-chariots), 大乘 (Mahayana Buddhism), and 史乘 (historical records). Modern everyday senses (ride, multiply) all stay chéng.
Components
ideograph
乘chéng
to ride; to multiply; vehicle
Single fused unit of ten interleaved strokes — the modern shape overlays cursive residues onto a 禾-like body so historical components no longer separate cleanly. Best learned as the silhouette behind 乘车, 乘客, and 乘法. Filed under Kangxi #4 丿 by tradition, with no visible radical-element in the modern form.
Filed under radical 丿 (piě, #4) by convention. 丿 is not a separate component in 乘, so no strokes are highlighted.
