Correct option is A. [\(\vec a\,\vec b\,\vec c\)] = 0
Here, \(\vec a\) lies in the plane of vectors \(\vec b\) and \(\vec c\), which means \(\vec a,\, \vec b\) and \(\vec c\) are coplanar.
We know that \(\vec b\times \vec c\) is perpendicular to \(\vec b\) and \(\vec c\).
Also dot product of two perpendicular vector is zero.
Since, \(\vec a,\,\vec b,\,\vec c\) are coplanar, \(\vec b\times \vec c\) is perpendicular to \(\vec a\).
So,