A random variable X $$\sim$$ B (n, p), if values of mean and variance of X are 18 and 12 respectively, then n =

The shortest distance between lines $$\bar{r}=(2 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$$ and $$\bar{r}=(\hat{r}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+\hat{j}-5 \hat{k})$$ is

The equation of perpendicular bisector of the line segment joining $$A(-2,3)$$ and $$B(6,-5)$$ is

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are mutually perpendicular vectors having magnitudes $$1,2,3$$ respectively, then $$\left[\begin{array}{lll}\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}} & \overline{\mathrm{b}}-\overline{\mathrm{a}} & \overline{\mathrm{c}}\end{array}\right]=$$