Two adjacent sides of a parallelogram \( \mathrm{ABCD} \) are given...

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Two adjacent sides of a parallelogram \( \mathrm{ABCD} \) 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 \( A D \)
\( \mathrm{P} \) is rotated by an acute angle \( \alpha \) in the plane of the

VV parallelogram so that \( \mathrm{AD} \) becomes \( \mathrm{AD}^{\prime} \). If \( \mathrm{AD}^{\prime} \) makes a right angle with the side \( \mathrm{AB} \), then the cosine of the angle \( \alpha \) is given by
(a) \( \frac{8}{9} \)
(b) \( \frac{\sqrt{17}}{9} \)
(c) \( \frac{1}{9} \)
(d) \( \frac{4 \sqrt{5}}{9} \)
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