I post this here because i see questions relating to torsion from this topic,but not in differential geometry.

If a curve is in a plane,say (x,y,3) is the torsion always =0 ?

Or let me try this visualisation; a fighter pilot flies in a jet at say 10 000 ft and stays at this altitude,but is doing barrel rolls,ie spiralling through the air,but still at ten thousand ft. Is the tortion of his curve zero?