3D Geometry

94 NDA Mathematics previous year questions (PYQs) from 19 papers, 2017 to 2026, with answers and worked solutions.

About this chapter

Difficulty: 27 easy · 46 moderate · 21 hard.
Most-asked subtopics: Direction Cosines and Ratios (25), Distance, Section, and Collinearity in 3D (22), Sphere (20).
Updated 14 September 2026.

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NDA · Sep 2026 · Q61Moderate
#1Distance, Section, and Collinearity in 3D
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NDA · Sep 2026 · Q63Moderate
#2Distance, Section, and Collinearity in 3D
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NDA · Apr 2017 · Q62Easy
#3Distance, Section, and Collinearity in 3D
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NDA · Apr 2017 · Q63Moderate
#4Distance, Section, and Collinearity in 3D
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NDA · Sep 2017 · Q42Easy
#5Distance, Section, and Collinearity in 3D
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NDA · Apr 2018 · Q58Hard
#6Distance, Section, and Collinearity in 3D
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NDA · Apr 2018 · Q61Hard
#7Distance, Section, and Collinearity in 3D
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NDA · Sep 2018 · Q56Easy
#8Distance, Section, and Collinearity in 3D
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NDA · Sep 2018 · Q57Hard
#9Distance, Section, and Collinearity in 3D
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NDA · Apr 2019 · Q61Easy
#10Distance, Section, and Collinearity in 3D
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NDA · Sep 2019 · Q60Moderate
#11Distance, Section, and Collinearity in 3D
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NDA · Apr 2020 · Q62Easy
#12Distance, Section, and Collinearity in 3D
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NDA · Apr 2020 · Q64Easy
#13Distance, Section, and Collinearity in 3D
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NDA · Apr 2021 · Q69Hard
#14Distance, Section, and Collinearity in 3D
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NDA · Sep 2021 · Q63Moderate
#15Distance, Section, and Collinearity in 3D
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NDA · Sep 2022 · Q62Moderate
#16Distance, Section, and Collinearity in 3D
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Set · 2 questions
Consider the following for the next two (02) items that follow: The position vectors of two points $A$ and $B$ are $\hat{i}-\hat{j}$ and $\hat{j}+\hat{k}$ respectively.
- NDA · Apr 2023 · Q69Moderate
  #17Distance, Section, and Collinearity in 3D
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- NDA · Apr 2023 · Q70Easy
  #18Distance, Section, and Collinearity in 3D
  Strategy Concept notes
NDA · Sep 2023 · Q96Moderate
#19Distance, Section, and Collinearity in 3D
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NDA · Sep 2023 · Q100Moderate
#20Distance, Section, and Collinearity in 3D
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NDA · Apr 2025 · Q62Hard
#21Distance, Section, and Collinearity in 3D
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NDA · Apr 2025 · Q63Hard
#22Distance, Section, and Collinearity in 3D
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NDA · Sep 2026 · Q62Hard
#23Direction Cosines and Ratios
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NDA · Apr 2017 · Q61Easy
#24Direction Cosines and Ratios
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NDA · Apr 2017 · Q65Moderate
#25Direction Cosines and Ratios
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NDA · Sep 2017 · Q43Moderate
#26Direction Cosines and Ratios
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NDA · Sep 2017 · Q53Moderate
#27Direction Cosines and Ratios
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NDA · Apr 2019 · Q65Easy
#28Direction Cosines and Ratios
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NDA · Sep 2019 · Q56Moderate
#29Direction Cosines and Ratios
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NDA · Sep 2019 · Q59Hard
#30Direction Cosines and Ratios
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NDA · Apr 2020 · Q63Easy
#31Direction Cosines and Ratios
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NDA · Apr 2021 · Q66Moderate
#32Direction Cosines and Ratios
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NDA · Apr 2021 · Q67Hard
#33Direction Cosines and Ratios
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NDA · Apr 2021 · Q68Easy
#34Direction Cosines and Ratios
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NDA · Sep 2021 · Q62Moderate
#35Direction Cosines and Ratios
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NDA · Sep 2021 · Q65Hard
#36Direction Cosines and Ratios
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NDA · Sep 2022 · Q64Moderate
#37Direction Cosines and Ratios
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NDA · Sep 2022 · Q65Easy
#38Direction Cosines and Ratios
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Set · 2 questions
Consider the following for the next two (02) items that follow: Consider two lines whose direction ratios are $(2,-1,2)$ and $(k,3,5)$ . They are inclined at an angle $\dfrac{\pi}{4}$ .
- NDA · Apr 2023 · Q63Hard
  #39Direction Cosines and Ratios
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- NDA · Apr 2023 · Q64Moderate
  #40Direction Cosines and Ratios
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NDA · Sep 2023 · Q98Moderate
#41Direction Cosines and Ratios
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NDA · Apr 2024 · Q54Moderate
#42Direction Cosines and Ratios
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NDA · Apr 2024 · Q57Moderate
#43Direction Cosines and Ratios
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Set · 2 questions
Let $S$ be the line of intersection of two planes $x+y+z=1$ and $2x+3y-4z=8$ with direction ratios $\langle -7,6,1\rangle$ . If $(l,m,n)$ are direction cosines of $S$ , then what is the value of $43l^2-m^2-n^2$ ?
- NDA · Sep 2024 · Q67Moderate
  #44Direction Cosines and Ratios
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- NDA · Sep 2024 · Q68Hard
  #45Direction Cosines and Ratios
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NDA · Apr 2025 · Q61Hard
#46Direction Cosines and Ratios
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NDA · Apr 2025 · Q64Moderate
#47Direction Cosines and Ratios
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NDA · Apr 2017 · Q64Moderate
#48The Straight Line in 3D
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NDA · Sep 2017 · Q52Easy
#49The Straight Line in 3D
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NDA · Sep 2018 · Q58Hard
#50The Straight Line in 3D
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