The unit vector perpendicular to the vectors $6i + 2j + 3k$ and $3i - 6j - 2k$ is

$A$ tetrahedron has vertices $P(1, 2, 1)$,$Q(2, 1, 3)$,$R(-1, 1, 2)$ and $O(0, 0, 0)$. The angle between the faces $OPQ$ and $PQR$ is

If $C$ is a given non-zero scalar and $\overline{A}$ and $\overline{B}$ are given non-zero vectors such that $\overline{A}$ is perpendicular to $\overline{B}$. If vector $\overline{X}$ is such that $\overline{A} \cdot \overline{X} = C$ and $\overline{A} \times \overline{X} = \overline{B}$,then $\overline{X}$ is given by:

$(a - b) \times (a + b) = $

If $a=\hat{i}+\hat{j}+\hat{k}$, $c=\hat{j}-\hat{k}$, $a \times b=c$ and $a \cdot b=3$, then $b$ is equal to

If $|a| = 4$,$|b| = 2$ and the angle between $a$ and $b$ is $\pi/6$,then find $|a \times b|^{2}$.