If \(\mathbf{a}\) and \(\mathbf{b}\) are respectively the internal and external bisectors of the angles between the vectors \(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}\) and \(|\mathbf{a}|=\frac{2}{3} \sqrt{6},|\mathbf{b}|=\frac{2}{3} \sqrt{3}\), then one of the values of \(\mathbf{a}-\mathbf{b}\) is

1. A \(\frac{1}{10}(-8 \hat{\mathbf{i}}+11 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})\)
2. B \(\frac{2}{3}(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})\)
3. C \(\frac{1}{15}(9 \hat{\mathbf{i}}-11 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\)
4. D \(\frac{1}{12}(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)