Two adjacent sides of a parallelogram ABCD are given by $\vec{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k}$ and $\vec{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}$. The side AD is rotated by an acute angle $\alpha$ in the plane of parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then $\cos \alpha =$
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Angle between two vectors $\vec{u}, \vec{v}$ is given by $\cos \theta = \frac{\vec{u} \cdot \vec{v}}{|\vec{u}||\vec{v}|}$.