The position vector of a point \(P\) is \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(\mathbf{b}\) and lying on the plane \(\pi\) is

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