The coordinates of the point at which the $XZ$-plane divides the line segment joining $A(-2, 3, 4)$ and $B(1, 2, 3)$ are:

If for some $m \in \mathbb{R}$ the lines $L_1 : \frac{x + 1}{m} = \frac{y - m}{-1} = \frac{z - 1}{1}$ and $L_2 : \frac{x + 2}{-4} = \frac{y + 1}{9} = \frac{z + 1}{1}$ are coplanar, then line $L_1$ passes through the point

If a point $P$ on the line segment joining the points $(3, 5, -1)$ and $(6, 3, -2)$ has its $y$-coordinate $2$,then its $z$-coordinate is

Find the equation of a line parallel to the $x$-axis and passing through the origin.

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

The angle between the pair of lines given by $\vec{r} = 3\hat{i} + 2\hat{j} - 4\hat{k} + \lambda(\hat{i} + 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} - 2\hat{k} + \mu(3\hat{i} + 2\hat{j} + 6\hat{k})$ is . . . . . . .