If $$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$$ and $$\overrightarrow{d}$$ are unit vectors such that $$(\overrightarrow{a}\times\overrightarrow{b}).(\overrightarrow{c}\times\overrightarrow{d})=1$$ and $$\overrightarrow{a}.\overrightarrow{c}=\frac{1}{2}$$ then

A

$$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$$ are non-coplanar

B

$$\overrightarrow{a},\overrightarrow{c},\overrightarrow{d}$$ are non-coplanar

C

$$\overrightarrow{b},\overrightarrow{d}$$ are non- parallel

D

$$\overrightarrow{a},\overrightarrow{d}$$ are parallel and $$\overrightarrow{b},\overrightarrow{c}$$