CUET · MATHS · PYQ PAPER 2023
The values of p for which the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 p}=\frac{y-5}{1}=\frac{6-z}{5}\) are at right angles is:
- A \(\frac{70}{11}\)
- B \(\frac{11}{70}\)
- C \(\frac{7}{11}\)
- D \(\frac{11}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{70}{11}\)
Step-by-step Solution
Detailed explanation
Direction ratios of the first line: \(\vec{d_1} = \left\langle -3, \frac{2p}{7}, 2 \right\rangle\) Direction ratios of the second line: \(\vec{d_2} = \left\langle -\frac{3p}{7}, 1, -5 \right\rangle\) For perpendicular lines: \(\vec{d_1} \cdot \vec{d_2} = 0\)…
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