If \(\mathbf{e}\) is a unit vector perpendicular to the plane determined by the points \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\). If \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}\), then the projection vector of \(\mathbf{a}\) on \(\mathbf{e}\) is

1. A \(\frac{11}{14}(-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}})\)
2. B \(\frac{1}{3}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})\)
3. C \(\frac{1}{7}(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})\)
4. D \(\frac{1}{\sqrt{14}}(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})\)