Final answer:
The problem discusses vector lengths and charges in a geometric context, comparing distances from points R, T, and S. Due to ambiguous information in the question, it's not possible to state the length of 'qrst sude qe.' The answer to the length of 'qrst sude qe' is not determinable from the options provided.
Step-by-step explanation:
The question provided seems to involve mathematical concepts, particularly those related to vectors and distances in a geometric context. Based on the information given, it talks about vectors that are closest to points R and T and compares their length to those around point S. The vectors near R and T start at approximately 4 units, whereas the vectors near S start at about 6 units.
Using the provided equations, where qr/d² = qs/D², and given that the charge on S is about twice that on R and T after the calculation (qr| d² = qs| D², so qs|| R = D² / d² = 36 / 16 = 2.25), we can determine that the context is likely about vector magnitudes in relation to electrical charges at distances.
However, it seems there is confusion with the reference of 'qrst sude qe.' There is no clear explanation for what this means in mathematical terms, and it may be a typo or an improperly formatted part of the question. Given that there is ambiguity in the term 'qrst sude qe,' it's not possible to accurately determine its length based solely on the information provided. If it relates to the distances from R or T, it could be 4 units; if it relates to S, it could be 6 units. The correct choice is not stated among the options given in this context.