The correct answer is B) 045.0°. A vessel heading northeast (NE) is on a course of 045.0° (or 45 degrees). This is because northeast is one of the cardinal directions, which are defined as the four principal compass points - north, east, south, and west. Northeast is the midpoint between north and east, and the direction corresponding to 45 degrees on a compass. The other answer choices are incorrect because 022.5° is northeast by north, 067.5° is east-northeast, and 090.0° is due east, which do not accurately represent a northeast heading.