CUET · MATHS · PYQ PAPER 2025
The shortest distance between the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{x-3}{4}\) and \(\frac{x-2}{4}=\frac{y-4}{6}=\frac{x-5}{8}\) is equal to:
- A \(0\)
- B \(\sqrt{\frac{29}{5}}\)
- C \(\sqrt{\frac{5}{29}}\)
- D \(\sqrt{5}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{5}{29}}\)
Step-by-step Solution
Detailed explanation
\(\vec{a_1} = \langle 1, 2, 3 \rangle\), \(\vec{d_1} = \langle 2, 3, 4 \rangle\) \(\vec{a_2} = \langle 2, 4, 5 \rangle\), \(\vec{d_2} = \langle 4, 6, 8 \rangle\) Since \(\vec{d_2} = 2\vec{d_1}\), the lines are parallel. Use \(\vec{d} = \vec{d_1}\).…
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