If $p$ is the shortest distance between the lines $\dfrac{x+1}{7} = \dfrac{y+1}{-6} = z+1$ and $\vec{r} = (3\hat{i} + 5\hat{j} + 7\hat{k}) + \mu(\hat{i} - 2\hat{j} + \hat{k})$ then $[p]$ is... ,(where $[\,.\,]$ denotes the greatest integer function.)

The symmetric form of the equation of the line $x = ay + b$, $z = cy + d$ is

The equation of the plane passing through the points having position vectors $(\bar{a} + \bar{b}), (\bar{b} + \bar{c})$ and $(\bar{a} + \bar{c})$ is $\ldots$

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 $\ldots$