Let \(\rm\vec{a},\vec{b},\vec{c}\) be three non zero vectors such that \(\rm \vec{c}\) is a unit vector perpendicular to both \(\rm \vec{a}\) and \(\rm \vec{b}\). If the angle between \(\rm\vec{a}\) and \(\rm\vec{b}\) be \(\frac{\pi}{6}\) then \(\begin{bmatrix} \vec{a} &\vec{b}& \vec{c}\end{bmatrix}^2 \) is:
1
\(\rm |\vec{a}|^2|\vec{b}|^2\)
2
\(\rm\frac{1}{2} |\vec{a}|^2|\vec{b}|^2\)
3
\(\rm\frac{1}{4} |\vec{a}|^2|\vec{b}|^2\)
4
\(\rm 2 |\vec{a}|^2|\vec{b}|^2\)