\(R\) divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(-\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively in the ratio \(2: 1\) externally. \(S\) divides \(P Q\) internally in the ratio \(2: 1\). Then, the position vector of the midpoint of the line joining \(R\) and \(S\) is

1. A \(\frac{-5}{3} \hat{\mathbf{i}}-\frac{2}{3} \hat{\mathbf{j}}-\frac{5}{3} \hat{\mathbf{k}}\)
2. B \(\frac{-5}{3} \hat{\mathbf{i}}+\frac{2}{3} \hat{\mathbf{j}}+\frac{5}{3} \hat{\mathbf{k}}\)
3. C \(\frac{5}{3} \hat{\mathbf{i}}-\frac{2}{3} \hat{\mathbf{j}}-\frac{5}{3} \hat{\mathbf{k}}\)
4. D \(\frac{5}{3} \hat{\mathbf{i}}+\frac{2}{3} \hat{\mathbf{j}}+\frac{5}{3} \hat{\mathbf{k}}\)