Two adjacent sides of a parallelogram ABCD are given by `vec(AB)=2hat(i)+10hat(j)+11hat(k)` and `vec(AD)=-hat(i)+2hat(j)+2hat(k)` . The side AD is rotated by an acute angle `alpha` in the plane of the parallelogram so that AD becomes AD' . If AD' makes a right angle with the side AB, then the cosine of the angle `alpha` is given by

Options

A. `(8)/(9)`
B. `(sqrt(17))/(9)`
C. `(1)/(9)`
D. `(4sqrt(5))/(9)`

Answer

B