Mathematics - Vector Question with Solution | TestHub

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