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 $\ldots$

The angle between the line $\bar{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})$ and the plane $\bar{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 8$ is $\ldots$

The acute angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is $\ldots$