Question

The lines \(\frac{x-1}{-1} = \frac{y+2}{1} = \frac{z-3}{-2}\) and \(\frac{x-1}{1} = \frac{y+2}{1} = \frac{z+1}{-2}\) are

• A. intersecting but not perpendicular
• B. parallel
• C. perpendicular
• D. skew lines

Hint:

Check parallel, perpendicular, then test the scalar triple product for intersection.

Answer 1

The Correct Option is D

Step 1: Find intersection attempt:
Equate: $1 - s = 1 + t$, $-2 + s = -2 + t$, $3 - 2s = -1 - 2t$.

Step 2: Solve:
From the first, $s = -t$. From the second, $s = t$, so $s = t = 0$. Third: $3 = -1$, which is false.

Step 3: Conclusion:
No common point exists, and the directions are not parallel, so the lines are skew, option (D).

Final Answer:
The lines are skew. \[ \boxed{\text{(D) }\text{skew lines}} \]