The length of the perpendicular drawn from the point $(1, 2, 3)$ to the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{-2}$ is:

The coordinates of the point of intersection of the lines $\frac{x - 3}{1} = \frac{y - 5}{2} = \frac{z - 1}{-1}$ and $\frac{x - 4}{2} = \frac{y - 2}{-1} = \frac{z - 4}{2}$ are:

If the line joining the points $A(7, p, 2)$ and $B(q, -2, 5)$ is parallel to the line joining the points $C(2, -3, 5)$ and $D(-6, -15, 11)$,then the value of $p^2 + q^2$ is equal to

The shortest distance between the lines $\overline{r} = (4\hat{i} - \hat{j}) + \lambda(\hat{i} + 2\hat{j} - 3\hat{k})$ and $\overline{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(2\hat{i} + 4\hat{j} - 5\hat{k})$ is:

The equation of a line passing through a point $(4, -2, 3)$ and perpendicular to the $XZ$-plane is:

$A(2,3,4), B(4,5,7), C(2,-6,3), D(4,-4, k)$ are four points. If the line $\overline{AB}$ is parallel to $\overline{CD}$,then $k$ is equal to