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CUET · MATHS · PYQ PAPER 2025

The value of p so that the lines \(\frac{x-1}{-3}=\frac{2 y-2}{2 p}=\frac{z-3}{2}\) and \(\frac{x-1}{-3 p}=\frac{y-1}{4}=\frac{6-z}{5}\) are at right angles is

  1. A \(-\frac{10}{17}\)
  2. B \(-\frac{10}{13}\)
  3. C \(\frac{10}{13}\)
  4. D \(\frac{10}{17}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{10}{13}\)

Step-by-step Solution

Detailed explanation

Direction vectors: \(\vec{d_1} = \langle -3, p, 2 \rangle\), \(\vec{d_2} = \langle -3p, 4, -5 \rangle\). For right angles, \(\vec{d_1} \cdot \vec{d_2} = 0\): \((-3)(-3p) + (p)(4) + (2)(-5) = 0\) \(9p + 4p - 10 = 0\) \(13p = 10\) \(p = \frac{10}{13}\)