If \(\vec{\mathrm{a}},\vec{\mathrm{b}},\ \vec{\mathrm{c}}\) and \(\vec{\mathrm{d}}\) are unit vectors such that \((\vec{\mathrm{a}}\times\vec{\mathrm{b}}).(\vec{\mathrm{c}}\times\vec{\mathrm{d}})=1\) and \(\displaystyle \vec{\mathrm{a}}.\vec{\mathrm{c}}=\frac{1}{2}\), then
1
\(\vec{\mathrm{a}},\vec{\mathrm{b}},\ \vec{\mathrm{c}}\) are non-coplanar
2
\(\vec{\mathrm{b}},\ \vec{\mathrm{c}},\vec{\mathrm{d}}\) are non-coplanar
3
\(\vec{\mathrm{a}},\vec{\mathrm{b}},\ \vec{\mathrm{c}}\) and \(\vec{d}\) are coplanar vectors
4
\(\vec{\mathrm{a}},\vec{\mathrm{d}}\) are parallel and \(\vec{\mathrm{b}},\ \vec{\mathrm{c}}\) are parallel