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Mathematics - Three Dimensional Geometry

Practise 57 COMEDK previous year questions on Three Dimensional Geometry, compiled from papers spanning 2012 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty COMEDK tests.

Three Dimensional Geometry has been asked in 10 of the 15 years of COMEDK papers analysed (2012–2026), with 57 questions in all. 30% of them were easy, 65% moderate and 5% tough. Most of its questions came from 2024, with 13 questions that year. In the last three years (2024–2026) it had 30 questions across 10 papers, about 3 per paper.

The chapter's 5 topics are not weighted equally: Line in Space (27 questions, 47%), Direction Cosines and Direction Ratios (15 questions, 26%), and Line and Plane (6 questions, 11%) have been asked the most. Line in Space has also led over the last five years, with 24 questions. Plane in Space has produced the most tough questions (2).

  1. 1Let L be the foot of the perpendicular drawn from the point to the YZ-plane. If the distance of point L from the origin is units, then the p09 May, 2026 (S1)Plane in Space
  2. 2Let P be a point on the line such that its distance from the point is 6 units. Given that -coordinate of P is greater than 2 , Find the coor09 May, 2026 (S1)Line in Space
  3. 3The angle between the two lines whose direction cosines satisfy the relations and is09 May, 2026 (S1)Direction Cosines and Direction Ratios
  4. 4Consider the lines and given by the following vector equations: If and the lines intersect, then the value of 't' is:09 May, 2026 (S2)Line in Space
  5. 5The equation of the perpendicular drawn from the point to the line is . If are the possible integers such that , then the value of is:09 May, 2026 (S2)Line in Space
  6. 6Consider two skew lines in 3D space. and Let be the line of shortest distance (common perpendicular) between and If is a line parallel to th09 May, 2026 (S2)Line in Space
  7. 7Given that the lines and are neither skew nor parallel. Then the shortest distance between the lines is25 May, 2025 (Shift)Line in Space
  8. 8The angle between the lines and is , then the value of is25 May, 2025 (Shift)Line in Space
  9. 9The foot of the perpendicular from the point to the line is25 May, 2025 (Shift)Line in Space
  10. 10A line passing through the point A with position vector is parallel to the vector . The length of the perpendicular drawn from a point P wit10 May, 2025 (S1)Line in Space
  11. 11The value of for which the angle between lines and is10 May, 2025 (S1)Line in Space
  12. 12P is a point on the line joining the points and . If coordinate of point P is 2 , then coordinate will be10 May, 2025 (S1)Basics of point in 3 dimension
  13. 13The length of the perpendicular from the point to the given line is10 May, 2025 (S2)Line in Space
  14. 14If is the image of the point in the line then is equal to10 May, 2025 (S2)Line in Space
  15. 15The image of a point in the line is . Then10 May, 2025 (S3)Line in Space
  16. 16The equation of a line passing through origin with direction angles is10 May, 2025 (S3)Direction Cosines and Direction Ratios
  17. 17Two lines and intersect at a point. Then the value of ' ' is10 May, 2025 (S3)Line in Space
  18. 18If the line is perpendicular to the line , then find the value of2024 (Afternoon Shift)Direction Cosines and Direction Ratios
  19. 19A line makes the same angle with each of the and -axes. If the angle , which it makes with the -axis is such that , then equals2024 (Afternoon Shift)Direction Cosines and Direction Ratios
  20. 20The lines and are2024 (Afternoon Shift)Line in Space
  21. 21If the straight lines and are intersecting then can have2024 (Evening Shift)Line in Space
  22. 22The measure of the angle between the lines and is2024 (Evening Shift)Direction Cosines and Direction Ratios
  23. 23The co-ordinate of the foot of the perpendicular from on the line joining and is2024 (Evening Shift)Line in Space
  24. 24The angle between the lines and is2024 (Memory Based)Direction Cosines and Direction Ratios
  25. 25If the lines and are perpendicular, then the value of is2024 (Memory Based)Direction Cosines and Direction Ratios
  26. 26The line is parallel to the plane2024 (Memory Based)Line and Plane
  27. 27The foot of the perpendicular from to the line is2024 (Morning Shift)Line in Space
  28. 28The vector whose magnitude is units which makes an angle of and with and - axis respectively is2024 (Morning Shift)Direction Cosines and Direction Ratios
  29. 29The vector equation of two lines are Then the shortest distance between them is2024 (Morning Shift)Line in Space
  30. 30is a point on the line segment joining the points and . If coordinate of is 5, then its co-ordinate is2024 (Morning Shift)Basics of point in 3 dimension
  31. 31The distance of the point from the line is2023 (Evening Shift)Line in Space
  32. 32If the direction ratios of two lines are given by and , then the angle between the lines is2023 (Evening Shift)Direction Cosines and Direction Ratios
  33. 33Preview not available - open to view this question.2023 (Evening Shift)Basics of point in 3 dimension
  34. 34The coordinates of the vertices of the triangle are and . The direction cosines of the median are2023 (Evening Shift)Direction Cosines and Direction Ratios
  35. 35The place is parallel to the line2023 (Memory Based)Line and Plane
  36. 36The lines and are perpendicular to each other, then equals to2023 (Memory Based)Line in Space
  37. 37If two lines and intersect at a point, then is equal to2023 (Memory Based)Line in Space
  38. 38The place is parallel to the line2023 (Morning Shift)Direction Cosines and Direction Ratios
  39. 39If two lines and intersect at a point, then is equal to2023 (Morning Shift)Line in Space
  40. 40The lines and are perpendicular to each other, then equals to2023 (Morning Shift)Direction Cosines and Direction Ratios
  41. 41The line is parallel to the plane2022Line and Plane
  42. 42The angle between the lines and is2022Line in Space
  43. 43The point of intersection of the lines and is2022Line in Space
  44. 44The line is parallel to the plane2021Line and Plane
  45. 45The equation of a plane passing through the line of intersection of the planes , and at a distance from the point is2021Line and Plane
  46. 46The angle between the lines and is2021Line in Space
  47. 47The point of intersection of the lines and is2021Line in Space
  48. 48If , then a vector perpendicular to and in the plane containing and is2020Plane in Space
  49. 49A vector perpendicular to the plane containing the points is2020Line and Plane
  50. 50The direction ratios of the line which is perpendicular to the lines and are2015Direction Cosines and Direction Ratios

Frequently Asked Questions

1.How many questions are available for Three Dimensional Geometry?

This chapter includes 57 questions compiled from COMEDK papers spanning 2012 to 2026.

2.Are these questions only from COMEDK, or from other exams too?

These are COMEDK questions specifically for the Three Dimensional Geometry chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Three Dimensional Geometry an important chapter for COMEDK Mathematics?

Three Dimensional Geometry has appeared in 10 of the 15 years of COMEDK papers covered here, with 57 questions across 19 papers - about 3 per paper it appears in.

4.What is the difficulty level of Three Dimensional Geometry questions in COMEDK?

Of the 57 questions analysed for this chapter, 30% are easy, 65% moderate and 5% tough. 2024 had the most, with 13 questions.

5.Which topics in Three Dimensional Geometry should I focus on?

These topics have carried the most weightage in Three Dimensional Geometry:

  • Line in Space - 27 questions (47%)
  • Direction Cosines and Direction Ratios - 15 questions (26%)
  • Line and Plane - 6 questions (11%)
  • Plane in Space has produced the most tough questions (2).
6.Is Three Dimensional Geometry's weightage in COMEDK going up or down?

Across all 19 papers analysed, Three Dimensional Geometry has averaged about 3.0 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 3.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.