Final answer:
The question about determining the value of k for the relation S={(-1,1), (2,1), (3,2)} is unclear without additional context. The provided references appear unrelated to the mathematical problem.
Step-by-step explanation:
To determine the value of k for which the relation S={(-1,1), (2,1), (3,2)} satisfies a given condition, we need additional context or a specific mathematical condition. However, it appears there might be some confusion. The references provided - such as 'k=0 (flat universe)', 'k>0 (closed universe)' and 'k<0 (open universe)' - apply to cosmological models rather than to simple relations in mathematics like the one given for S. Similarly, discussion about concentrations, rates, unit vectors, transformations, and sine functions seems unrelated to the original question about the relation S.
Without the specific context or condition that k must satisfy for the relation S, it's not possible to provide a value of k. If the student can provide the correct context or full question details, we may be able to assist further.