\(P\) and \(Q\) are points on the straight line passing through the point \(A(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) and parallel to the vector \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\), If \(A P=A Q=3\), then the vector equation of the plane \(O P Q\) is

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