Two adjacent sides of a parallelogram ABCD are given by $\overrightarrow{A B}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overrightarrow{A D}=-\hat{i}+2 \hat{j}+2 \hat{k}$. The side AD is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that AD becomes $\mathrm{AD}^{\prime}$. If $\mathrm{AD}^{\prime}$ makes a right angle with the side AB , then the cosine of the angle $\alpha$ is given by