If the lines \( \displaystyle\frac{x+1}{3}=\displaystyle\frac{y+3}{5}=\displaystyle\frac{z+\lambda}{7} \) and \( \displaystyle\frac{x-2}{1}=\displaystyle\frac{y-4}{3}=\displaystyle\frac{z-6}{5} \) are intersecting , then the value of ‘\( \lambda \)’ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
A general point on each line is
\( L_1:\;(3t-1,\;5t-3,\;7t-\lambda) \)
\( L_2:\;(s+2,\;3s+4,\;5s+6) \)
At the point of intersection the x- and y-coordinates are equal:
\( 3t-1=s+2,\quad s=3t-3 \)
\( 5t-3=3(3t-3)+4=9t-5 \)
\( \displaystyle t=\frac{1}{2},\quad s=-\frac{3}{2} \)
The z-coordinates must also be equal:
\( \displaystyle \frac{7}{2}-\lambda=5\left(-\frac{3}{2}\right)+6=-\frac{3}{2} \)
\( \lambda=5 \)