Vector Algebra

Two adjacent sides of a parallelogram ABCD are given by

→

AB

= 2

^

i

+10

^

j

+11

^

k

and

→

AD

= −

^

i

+2

^

j

+2

^

k

. The side AD is rotated by an acute angle α 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 α is given by