The equations of two straight lines are $\frac{x-1}{2}=\frac{y+3}{1}=\frac{z-2}{-3}$ and $ \frac{x-2}{1}=\frac{y-1}{-3}=\frac{z+3}{2}$

Statement-1 : The given lines are coplanar.

Statement-2 : The equations

2r - s = 1

r + 3s = 4

3r + 2s = 5

are consistent.

Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

The coordinates of arbitrary positions of the given lines are (2r + 1, r-3, -3r + 2) and (s + 2, -3s + 1, 2s - 3) respectively.

Given lines will intersect (be coplanar) if

$2r + 1 = s + 2, r- 3= - 3s + 1 $ and $-3r + 2 = 2s - 3 $

are consistent i.e. 2r - s = 1, 3s = 4 and 3r + 2s = 5 are consistent.

Clearly, values of r and s obtain from any two equations satisfy the third equation. So, these equations are consistent.

Hence, both the statements are true and statement-2 is a correct explanation for statement-1.