CUET UG 2025 — Mathematics Geometry
The vector equation of line passing through (2, -1, 3) and perpendicular to the lines
3x−2=1y−1=2z+2 and −4x+3=−3y−5=2z+1 is
(Here λ is a parameter)
Held on 29 May 2025 · Verified 13 Jul 2026.
r=(2i^−j^+3k^)+λ(8i^−14j^−5k^)
r=(−2i^+j^−3k^)+λ(8i^−14j^−5k^)
r=(−8i^−14j^−5k^)+λ(−2i^+j^+3k^)
r=(8i^−14j^−5k^)+λ(2i^−j^+3k^)
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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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