CUET · MATHS · PYQ PAPER 2023
If the lines \(\frac{x+3}{k-5}=\frac{y-1}{1}=\frac{5-z}{-2 k-1}\) and \(\frac{x+2}{-1}=\frac{2-y}{-k}=\frac{z}{5}\) are perpendicular, then the value of \(k\) is
- A 1
- B -1
- C 2
- D -2
Answer & Solution
Correct Answer
(B) -1
Step-by-step Solution
Detailed explanation
\( \vec{d_1} = (k-5, 1, 2k+1) \) \( \vec{d_2} = (-1, k, 5) \) \( \vec{d_1} \cdot \vec{d_2} = 0 \) \( (k-5)(-1) + (1)(k) + (2k+1)(5) = 0 \) \( -k+5 + k + 10k+5 = 0 \) \( 10k+10 = 0 \) \( 10k = -10 \) \( k = -1 \)
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