CUET UG 2025 — Mathematics Geometry
Consider a line r=(i^+4j^)+λ(2i^−2j^+3k^), then which of the following statements are correct?
(A) it passes through point (9, -4, 12)
(B) it passes through point (1, 4, -1)
(C) its direction cosine's are 172,17−2,173
(D) its Cartesian equation is 2x−1=−2y−4=3z
Choose the correct answer from the options given below:
Held on 14 May 2025 · Verified 13 Jul 2026.
(A), (C) and (D) only
(B) and (C) only
(A) and (C) only
(B) and (D) 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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