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Consider two lines l_1 and l_2 with cartesian equations x 2 = 1-y -2 = z 1 and 2x-5 16 = y-2 -1 = z-5 4 respectively. Which of the following is/are…

CUET UG 2025 — Mathematics Geometry

2025mcqhard

Consider two lines l1l_1l1​ and l2l_2l2​ with cartesian equations x2=1−y−2=z1\frac{x}{2} = \frac{1-y}{-2} = \frac{z}{1}2x​=−21−y​=1z​ and 2x−516=y−2−1=z−54\frac{2x-5}{16} = \frac{y-2}{-1} = \frac{z-5}{4}162x−5​=−1y−2​=4z−5​ respectively. Which of the following is/are true?

(A) Direction ratio of l1l_1l1​ are 2, 2, 1
(B) Direction cosines of l1l_1l1​ are 23,−23,13\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}32​,3−2​,31​
(C) Direction ratio of l2l_2l2​ are 16, -1, 4
(D) Angle between l1l_1l1​ and l2l_2l2​ is cos⁡−1(383273)\cos^{-1}\left(\frac{38}{3\sqrt{273}}\right)cos−1(3273​38​)

Choose the correct answer from the options given below:

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (B), (C) and (D) only

  2. B

    (A) and (B) only

  3. C

    (C) and (D) only

  4. D

    (A) only

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