CUET · MATHS · PYQ PAPER 2025
If the lines \(\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{\lambda}\) and \(\frac{x}{1}=\frac{y}{2 \lambda}=\frac{z}{3}\) are perpendicular to each other, then \(\lambda\) is equal to
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\( \vec{d_1} = (7, -5, \lambda) \), \( \vec{d_2} = (1, 2\lambda, 3) \) \( \vec{d_1} \cdot \vec{d_2} = 0 \) \( (7)(1) + (-5)(2\lambda) + (\lambda)(3) = 0 \) \( 7 - 10\lambda + 3\lambda = 0 \) \( 7 - 7\lambda = 0 \) \( 7\lambda = 7 \) \( \lambda = 1 \)
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