Vector Algebra

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