Chapter 16: Problem 24
Two adjacent sides of a parallelogram \(\mathrm{ABCD}\) are given by \(\overrightarrow{\mathrm{AB}}=2 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{AD}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) The side \(\mathrm{AD}\) is rotated by an acute angle \(\alpha\) in the plane of the 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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