If $2x - y + z = 0 = y - x + 2z = mx - 2y + mz$ represents a line in space,then the value of $m$ is-

The sum of the coordinates of one of the points on the line $\frac{x - 2}{1} = \frac{y + 3}{-2} = \frac{z + 5}{2}$ which is at a distance of $3 \text{ units}$ from the point $(2, -3, -5)$ is

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-2}{1}=\frac{y+m}{2}=\frac{z-2}{1}$ intersect each other,then the value of $m$ is

Find the shortest distance between the lines $\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}$ and $\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$.

The $xy$-plane divides the line segment joining the points $(2, 4, 5)$ and $(-4, 3, -2)$ in the ratio:

If $(a, b, c)$ is the image of the point $(1, 2, -3)$ in the line $\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1}$,then $a+b+c$ is equal to