If a parallelogram is constructed on the vectors $\bar{a} = 3\bar{p} - \bar{q}, \bar{b} = \bar{p} + 3\bar{q}$ and $|\bar{p}| = 3, |\bar{q}| = 2$ and angle between $\bar{p}$ and $\bar{q}$ is $\dfrac{\pi}{3}$, then the ratio of the lengths of adjacent sides $\bar{a}$ and $\bar{b}$ of the parallelogram is

A vector $\bar{r}$ of magnitude $3\sqrt{2}$ units which makes angles of $\dfrac{\pi}{4}$ and $\dfrac{\pi}{2}$ respectively with Y and Z axes is

The point having position vector $4\hat{i} - 11\hat{j} + 2\hat{k}$ lies on the line

The shortest distance between the lines, where the first line passes through $(0,0,0)$ and $(2,0,3)$ and the second line passes through $(2,5,0)$ and $(0,4,0)$ is