Question

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....

• A. \(1\)
• B. \(2\)
• C. \(-1\)
• D. \(4\)

Hint:

Lines intersect when the scalar triple product of the join vector and both directions is zero.

Answer 1

The Correct Option is C

Step 1: Solve using parameters
Set $1+2s=2+t$, $-1+3s=-m+2t$, $1+4s=2+t$. The first and third give $2s=4s$, so $s=0$, $t=-1$.
Then $-1=-m-2$, so $m=-1$. Option (C).

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]