$[i, k, j] + [k, j, i] + [j, k, i]$

If $\vec p$ and $\vec q$ are unit vectors such that $[\vec p, \vec q, \vec p \times \vec q] = \frac{1}{2}$,then the angle between $\vec p$ and $\vec q$ is

If $\overline{a}, \overline{b}, \overline{c}$ are mutually perpendicular vectors having magnitudes $1, 2, 3$ respectively,then the value of $[\overline{a}+\overline{b}+\overline{c} \quad \overline{b}-\overline{a} \quad \overline{c}]$ is

If $\vec{a}, \vec{b}, \vec{c}$ are non-zero and non-coplanar vectors such that $(\vec{a} + \lambda \vec{b}) \cdot [(\vec{b} + 3\vec{c}) \times (\vec{c} - 4\vec{a})] = 0$,then $\lambda$ is equal to

$a, b, c$ are three non-zero,non-coplanar vectors and $p, q, r$ are three other vectors such that $p = \frac{b \times c}{a \cdot (b \times c)}$,$q = \frac{c \times a}{a \cdot (b \times c)}$,$r = \frac{a \times b}{a \cdot (b \times c)}$. Then $[p, q, r]$ equals

If $a, b, c$ are three non-coplanar vectors,then $\frac{a \cdot (b \times c)}{c \times a \cdot b} + \frac{b \cdot (a \times c)}{c \cdot (a \times b)} = $