If the lines \( \displaystyle\frac{x-1}{2}=\displaystyle\frac{y-m}{3}=\displaystyle\frac{z-3}{4} \) and \( \displaystyle\frac{x-4}{5}=\displaystyle\frac{y-1}{2}=z \) are intersecting, then the value of \( m \), is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
General points on the two lines are
\( \displaystyle (2s+1,\ 3s+m,\ 4s+3)\quad\text{and}\quad(5t+4,\ 2t+1,\ t) \)
At the point of intersection the coordinates are equal. The z-coordinates give
\( \displaystyle t=4s+3 \)
and then the x-coordinates give
\( \displaystyle 2s+1=5(4s+3)+4 \)
\( \displaystyle 2s+1=20s+19 \)
\( \displaystyle s=-1,\quad t=-1 \)
Now the y-coordinates must be equal:
\( \displaystyle 3(-1)+m=2(-1)+1 \)
\( \displaystyle m-3=-1 \)
\( \displaystyle m=2 \)