If $\vec{a}, \vec{b}, \vec{c}$ 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
Select the correct option:
A
$\vec{a}, \vec{b}, \vec{c}$ are non-coplanar
B
$\overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}, \overrightarrow{\mathrm{d}}$ 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
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