The perpendicular distance from the point $P(-1, 1, 0)$ to the line joining the points $A(0, 2, 4)$ and $B(3, 0, 1)$ is

The lines $\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3 \hat{i} - \hat{j})$ and $\bar{r} = (4 \hat{i} - \hat{k}) + \mu(2 \hat{i} + 3 \hat{k})$ are

If the lines $\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5}$ are at right angles,then $k =$

If the lines given by $\bar{r} = 2 \hat{i} + \lambda(\hat{i} + 2 \hat{j} + m \hat{k})$ and $\bar{r} = \hat{i} + \mu(2 \hat{i} + \hat{j} + 6 \hat{k})$ are perpendicular,then the value of $m$ is:

The angle between the straight lines $\frac{x - 2}{2} = \frac{y - 1}{5} = \frac{z + 3}{-3}$ and $\frac{x + 1}{-1} = \frac{y - 4}{8} = \frac{z - 5}{4}$ is

If the lines $\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}$ and $\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}$ intersect,find the value of $k$.