If the lines \(\displaystyle\frac{x-1}{-3}=\frac{y-2}{2\lambda}=\frac{z-3}{2}\) and \(\displaystyle\frac{x-1}{3\lambda}=\frac{y-1}{2}=\frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −2
The direction ratios are read from the denominators:
\(\text{first line: } (-3,\ 2\lambda,\ 2)\)
\(\text{second line: } (3\lambda,\ 2,\ -5)\)
Two lines are perpendicular when \(a_1a_2 + b_1b_2 + c_1c_2 = 0\):
\((-3)(3\lambda) + (2\lambda)(2) + (2)(-5) = 0\)
\(-9\lambda + 4\lambda - 10 = 0\)
\(-5\lambda = 10\)
\(\lambda = -2\)