And are two lines whose vector equations are and where

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

Problem

L_1

and

L_2

are two lines whose vector equations are

L_1: r = \lambda[(\cos \theta + \sqrt{3})i + (\sqrt{2} \sin \theta)j + (\cos \theta - \sqrt{3})k]

and

L_2: r = \mu(ai + bj + ck)

where,

\lambda

and

\mu

are scalars and

\alpha

is the acute angle between

L_1

and

L_2

. If the angle

\alpha

is independent of

\theta

, then the value of

\alpha

is (1)

\frac{\pi}{6}

(2)

\frac{\pi}{4}

(3)

\frac{\pi}{3}

(4)

\frac{\pi}{2}