If $i, j, k$ are the unit vectors and mutually perpendicular,then $[i, k, j]$ is equal to

If $[\vec{a} \, \vec{b} \, \vec{c}] = 0$,then:

If $\bar{a}=\hat{i}+5 \hat{k}, \bar{b}=2 \hat{i}+3 \hat{k}, \bar{c}=4 \hat{i}-\hat{j}+2 \hat{k}$ and $\bar{d}=\hat{i}-\hat{j}$,then $(\bar{c}-\bar{a}) \cdot(\bar{b} \times \bar{d})=$

For what value of $a$ is the volume of the parallelepiped formed by the vectors $i + aj + k$,$j + ak$,and $ai + k$ minimum?

Let the volume of tetrahedron $ABCD$ be $81$ cubic units and $G_1, G_2, G_3$ be the centroids of the triangular faces $ABC, ABD,$ and $ACD$ respectively. Then the volume of tetrahedron $AG_1G_2G_3$ is (in cubic units):

Observe the following statements:
$A$. Three vectors are coplanar if one of them is expressible as a linear combination of the other two.
$R$. Any three coplanar vectors are linearly dependent.
Then, which of the following is true?