Vector Algebra

The position vectors of the points \(A\) and \(B\) with respect to \(O\) are \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\). The length of the internal bisector of \(\angle B O A\) of \(\triangle A O B\) is (take proportionality constant is 2)