If $|\bar{a}| = |\bar{b}| = 1, |\bar{c}| = 2$ and $\bar{a} \times (\bar{a} \times \bar{c}) + \bar{b} = \bar{0}$, then the acute angle between $\bar{a}$ and $\bar{c}$ is $\ldots$

The value of $|\bar{a} \cdot \bar{b}|^2 + |\bar{a} \times \bar{b}| \cdot |\bar{a} \times \bar{b}|$ is $\ldots$

If $\bar{a} \cdot \bar{b} = \beta$ and $\bar{a} \times \bar{b} = \bar{c}$ then $\bar{a} = $

If the equation of a plane passing through $A(1, p, 2)$, $B(3, 2, 4)$ and parallel to the z axis, is $3x - 2y - q = 0$, then $\ldots$