Final answer:
The question pertains to finding the relative position of two boats using vector subtraction. The correct bearings and directions must be used for vector representation, and subtracting the vectors graphically would reveal the final position of the woman compared to the dock after the mistake.
Step-by-step explanation:
To find out how far apart boats A and B are, we need to perform vector subtraction as per the given instructions in the question. We have two vectors, vector A and vector B, which represent the two legs of the trip to the dock. Their resultant vector, if one is reversed (traveling in the opposite direction), would give us the actual position relative to the dock.
In the scenario described, the woman first sails 27.5 meters at a bearing of 66.0° north of east. This is represented by vector A. She then is supposed to sail 30.0 meters at a bearing of 112° north of east (vector B), but instead, she mistakenly travels in the opposite direction. To represent this opposite direction, we use vector -B which has the same magnitude but opposite direction, at a bearing of 68° south of east (180° - 112° = 68°).
The final position of the woman, if the mistake occurs, would be found by adding vector A to vector -B (A - B). Using vector subtraction graphically, she would end up at a different location than the dock, illustrating the importance of following correct directions when traveling.