Two adjacent sides of a parallelogram are given by and

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Two adjacent sides of a parallelogram

ABCD

are given by

\vec{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k}

and

\vec{AD} = -\hat{i} + 2\hat{j} + 2\hat{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 (1)

\frac{8}{9}

(2)

\frac{\sqrt{17}}{9}

(3)

\frac{1}{9}

(4)

\frac{4\sqrt{5}}{9}