First rewrite both lines in standard form (C). Then apply perpendicularity condition (dot product = 0) on direction ratios (B). Simplify to get equation in p (D). Further simplify (E). Finally solve to get p=70/11 (A).
CUET UG 2022 — Mathematics Geometry
The correct order of steps from A to E, for finding value of p, so that the lines 31−x=2p7y−14=2z−3 and 3p7−7x=1y−5=56−z are at right angle is:
A. p=1170
B. (−3)×(7−3p)+1×(72p)+2×(−5)=0
C. −3x−1=27py−2=2z−3, −73px−1=1y−5=−5z−6
D. 79p+72p−10=0
E. 711p=10
Choose the correct answer from the options given below:
Held on 16 Jul 2022 · Verified 13 Jul 2026.
C, D, E, A, B
C, D, A, B, E
A, B, C, D, E
C, B, D, E, A
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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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