Trisection points divide segment in ratios 1:2 and 2:1.
For ratio 1:2: (31⋅1+2⋅1,31⋅3+2⋅0,31⋅2+2⋅2)=(1,1,2).
For ratio 2:1: (32⋅1+1⋅1,32⋅3+1⋅0,32⋅2+1⋅2)=(1,2,2).
So B and C.
CUET UG 2022 — Mathematics Geometry
The points of trisection of the segment joining the points (1, 0, 2) and (1, 3, 2) are:
A. (1,23,34)
B. (1, 1, 2)
C. (1, 2, 2)
D. (1,23,2)
Choose the correct answer from the options given below:
Held on 4 Aug 2022 · Verified 13 Jul 2026.
A and B only
B and D only
B and C only
A 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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