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.
Answer & explanation
Correct answer: option 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.