Mathematics

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 a.

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

are non-coplanar b.

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

are non-coplanar c.

\vec{b}, \vec{d}

are non-parallel d.

\vec{a}, \vec{d}

are parallel and

\vec{b}, \vec{c}

are parallel