A line passing through the points $(1, -1, 2)$ and $(2, 0, 1)$ meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...

The plane $\dfrac{x}{2} + \dfrac{y}{3} + \dfrac{z}{4} = 1$ cuts the axes at the points A, B, C then the area of triangle ABC is

From a point P $(a, b, c)$, perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OAB is

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.)