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CUET · MATHS · PYQ PAPER 2023

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then the value of \(\lambda\) is:

  1. A \(-\frac{7}{10}\)
  2. B \(-\frac{10}{7}\)
  3. C \(\frac{10}{7}\)
  4. D \(\frac{7}{10}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-\frac{10}{7}\)

Step-by-step Solution

Detailed explanation

Direction vectors: \( \vec{d_1} = \langle -3, 2\lambda, 2 \rangle \), \( \vec{d_2} = \langle 3\lambda, 1, -5 \rangle \) \( \vec{d_1} \cdot \vec{d_2} = 0 \) \( (-3)(3\lambda) + (2\lambda)(1) + (2)(-5) = 0 \) \( -9\lambda + 2\lambda - 10 = 0 \) \( -7\lambda = 10 \)…