The correct answer is B) 045.0°. A vessel heading in the northeast (NE) direction would be traveling on a compass course of 045.0°. This is because the northeast heading is directly in between the north (N) and east (E) cardinal directions, which are 000.0° and 090.0° respectively. The midpoint between these two cardinal directions is 045.0°, which represents the compass course for a vessel heading northeast. The other answer choices are incorrect because they do not accurately represent the compass course for a northeast heading. Option A (022.5°) is too far to the north, Option C (067.5°) is too far to the east, and Option D (090.0°) represents an easterly heading, which is not the same as a northeast heading.