If the lines \(\displaystyle\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\displaystyle\frac{x}{1}=\frac{y}{2\lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
The direction ratios of the lines are \(7, -5, \lambda\) and \(1, 2\lambda, 3\). Two lines are perpendicular when \(a_1a_2 + b_1b_2 + c_1c_2 = 0\):
\(7(1) + (-5)(2\lambda) + \lambda(3) = 0\)
\(7 - 10\lambda + 3\lambda = 0\)
\(7\lambda = 7,\quad \lambda = 1\)