Direction vectors d1=(1,−1,1), d2=(−1,1,−1)=−d1, so lines are parallel (B). Vector joining points: (1,−3,−4). Cross product with d1 gives (−7,−5,2) with magnitude 78. Distance = 78/3=26 (D).
CUET UG 2022 — Mathematics Geometry
The two lines given by r=(i^+2j^+3k^)+μ(i^−j^+k^) and r=(2i^−j^−k^)+μ(−i^+j^−k^)
A. are perpendicular
B. are parallel.
C. have shortest distance 0.
D. have shortest distance 26.
E. have shortest distance 78.
Which of the above statements are true?
Choose the correct answer from the options given below:
Held on 16 Jul 2022 · Verified 13 Jul 2026.
A and D only
B and D only
B and C only
B and E 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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