Which of the following points lie on the plane passing through \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}, 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) ?

1. A \(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\frac{5}{2} \hat{\mathbf{k}}\)
2. B \(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}}\)
3. C \(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\frac{3}{2} \hat{\mathbf{j}}+\frac{5}{2} \hat{\mathbf{k}}\)
4. D \(2 \hat{\mathbf{i}}+6 \hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\frac{3}{2} \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)