Final answer:
The question involves matching vector field diagrams with physical examples and using graphical methods to find resultant vectors, applying vector addition and subtraction techniques such as the head-to-tail method
Step-by-step explanation:
The student's question is related to vector fields and graphical methods for finding resultant vectors. To address the question, students must match plots to the correct vector fields and use vector addition or subtraction techniques to find the resultants of different vector combinations using the head-to-tail method or by calculating scalar products for certain pairs of vectors.
Matching the plots to the vector fields involves recognizing the patterns of the vector lines or the alignment of forces represented in the diagrams. For instance, a circular current loop's field (similar to a bar magnet) would match a vector field where the lines curve around in closed loops, pointing from a north to a south pole.
For calculations of the resultants, the graphical method requires drawing vectors to scale, placing them head to tail, and then drawing a vector from the start of the first vector to the end of the last vector, representing the resultant vector. This method also applies to the subtraction of vectors or multiplying them by scalars, such as in steps (e) to (h) of the question.