If and are unit vectors such that and

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

Problem

\vec{a}, \vec{b}, \vec{c}

and

\vec{d}

are unit vectors such that

(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) = 1

and

\vec{a} \cdot \vec{c} = \frac{1}{2}

, then (1)

\vec{a}, \vec{b}, \vec{c}

are non-coplanar (2)

\vec{a}, \vec{b}, \vec{d}

are non-coplanar (3)

\vec{b}, \vec{d}

are non-parallel (4)

\vec{a}, \vec{d}

are parallel and

\vec{b}, \vec{c}

are parallel