CUET UG 2025 — Mathematics Geometry
Consider two lines l1 and l2 with cartesian equations 2x=−21−y=1z and 162x−5=−1y−2=4z−5 respectively. Which of the following is/are true?
(A) Direction ratio of l1 are 2, 2, 1
(B) Direction cosines of l1 are 32,3−2,31
(C) Direction ratio of l2 are 16, -1, 4
(D) Angle between l1 and l2 is cos−1(327338)
Choose the correct answer from the options given below:
Held on 13 May 2025 · Verified 13 Jul 2026.
(B), (C) and (D) only
(A) and (B) only
(C) and (D) only
(A) only
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Consider the line $\vec{r} = -2\hat{i} + 3\hat{j} + \hat{k} + \lambda(5\hat{i} - 3\hat{j} - \hat{k})$. Match List-I with List-II | List-I | List-II | |---|---| | (A) A point on the given line | (I) $\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)$ | | (B) Direction ratios of the given line | (II) (2, 3, 1) | | (C) Direction cosines of the given line | (III) (5, -3, -1) | | (D) Direction ratios of a line perpendicular to given line | (IV) (-2, 3, 1) | Choose the correct answer from the options given below:
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