Jump to a section

Mathematics - Three Dimensional Geometry

Practise 418 JEE Main previous year questions on Three Dimensional Geometry, compiled from papers spanning 2002 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 JEE Main tests.

Three Dimensional Geometry has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 418 questions in all. 30% of them were easy, 55% moderate and 15% tough. Most of its questions came from 2023, with 71 questions that year. In the last three years (2024–2026) it had 95 questions across 49 papers, about 1.9 per paper.

The chapter's 5 topics are not weighted equally: Line in Space (183 questions, 44%), Plane in Space (137 questions, 33%), and Line and Plane (72 questions, 17%) have been asked the most. Line in Space has also led over the last five years, with 143 questions. Line in Space has produced the most tough questions (24).

  1. 1Let the foot of perpendicular from the point on the line be the point . Then the distance between the lines and is equal to:08 Apr, 2026 (E)Line in Space
  2. 2Let a line pass through the origin and be perpendicular to the lines and , . If , , is the point on at a distance of from the point of inter08 Apr, 2026 (E)Line in Space
  3. 3Let the image of the point in the line , , be . If , , is the point on such that the distance of from the foot of perpendicular from the poi06 Apr, 2026 (M)Line in Space
  4. 4Let a line be perpendicular to both the lines and . If is the acute angle between the lines and , then is equal to:06 Apr, 2026 (M)Line in Space
  5. 5The shortest distance between the lines and is :06 Apr, 2026 (E)Line in Space
  6. 6Let the image of the point in the line be the point and the image of the point in the line be the point . Then the square of the area of the06 Apr, 2026 (E)Line in Space
  7. 7The square of the distance of the point from the line is equal to:05 Apr, 2026 (M)Line in Space
  8. 8The square of the distance of the point of intersection of the lines , and from the origin is:05 Apr, 2026 (M)Line in Space
  9. 9Let a triangle be such that and lie on the line and are at a distance of units from . If is the centroid of , then is equal to :05 Apr, 2026 (E)Line in Space
  10. 10If the distance of the point from the image of the point in the line is , then the sum of all possible values of is equal to :05 Apr, 2026 (E)Line in Space
  11. 11A line with direction ratios intersects the lines and at the points and , respectively. If the length of the line segment is , then is equal04 Apr, 2026 (M)Line in Space
  12. 12The square of the distance of the point from the line along the line is equal to:04 Apr, 2026 (M)Line in Space
  13. 13The shortest distance between the lines and , , is:04 Apr, 2026 (E)Line in Space
  14. 14If is the image of in the line , then the possible value(s) of is (are)04 Apr, 2026 (E)Line in Space
  15. 15If the point of intersection of the lines and lies on -plane, then the value of is :02 Apr, 2026 (M)Line in Space
  16. 16Let a line passing through the point be perpendicular to both the vectors and . If is the foot of perpendicular from the origin on the line 02 Apr, 2026 (M)Line in Space
  17. 17Let the point A be the foot of perpendicular drawn from the point on the line . If the midpoint of the line segment PA is , then the value o02 Apr, 2026 (E)Line in Space
  18. 18If the distances of the point from the line along the lines and are equal, then is equal to28 Jan, 2026 (M)Line in Space
  19. 19Let be the image of the point in the line . Then the distance of Q from the line is28 Jan, 2026 (E)Line in Space
  20. 20If the distance of the point , from the line along a line with direction ratios is , then is equal to28 Jan, 2026 (E)Line in Space
  21. 21Let the lines and , intersect at the point R. Let P and Q be the points lying on lines and , respectively, such that and . If the point P li24 Jan, 2026 (M)Line in Space
  22. 22Let a line L passing through the point be perpendicular to the lines and . Let the line L intersect the plane at the point Q. Another line p24 Jan, 2026 (M)Line in Space
  23. 23The sum of all values of , for which the shortest distance between the lines and is , is24 Jan, 2026 (E)Line in Space
  24. 24Let the direction cosines of two lines satisfy the equations : and . Then the cosine of the acute angle between these lines is :23 Jan, 2026 (M)Direction Cosines and Direction Ratios
  25. 25The vertices B and C of a triangle ABC lie on the line . The coordinates of A and B are and respectively and C is at a distance of 10 units 23 Jan, 2026 (M)Line in Space
  26. 26If the image of the point in the line is Q and the image of Q in the line is P, then is equal to .23 Jan, 2026 (E)Line in Space
  27. 27If the image of the point in the line is , then is equal to22 Jan, 2026 (M)Line in Space
  28. 28Let be the point on the line at a distance from the point and nearer to the origin. Then the shortest distance, between the lines and , is e22 Jan, 2026 (M)Line in Space
  29. 29Let L be the line and let S be the set of all points on L, whose distance from the line along the line is 7. Then is equal to :22 Jan, 2026 (E)Line in Space
  30. 30Let be the co-ordinates of the foot of the perpendicular drawn from the point on the line . Then the length of the projection of the vector 21 Jan, 2026 (M)Line in Space
  31. 31Let the line pass through the point and make equal angles with the positive coordinate axes. If the distance of L from the point is , then t21 Jan, 2026 (E)Line in Space
  32. 32Let the line be parallel to the vector and pass through the point (2,6,7), and the line be parallel to the vector and pass through the point21 Jan, 2026 (E)Line in Space
  33. 33Let the values of for which the shortest distance between the lines and is be and . Then the radius of the circle passing through the points08 Apr, 2025 (E)Line in Space
  34. 34Let the area of the triangle formed by the lines and be . Then is equal to ________08 Apr, 2025 (E)Line in Space
  35. 35If the shortest distance between the lines and is , then the sum of all possible values of is07 Apr, 2025 (M)Line in Space
  36. 36Let the line L pass through and intersect the lines and . Then, which of the following points lies on the line L ?07 Apr, 2025 (M)Line in Space
  37. 37Consider the lines and . Let the feet of the perpendiculars from the point on the lines and be and respectively. If the area of the triangle07 Apr, 2025 (E)Line in Space
  38. 38If the equation of the line passing through the point and perpendicular to the lines and is , then is equal to :07 Apr, 2025 (E)Line in Space
  39. 39Let the shortest distance between the lines and be . Then the positive value of is04 Apr, 2025 (M)Line in Space
  40. 40Let A and B be two distinct points on the line . Both A and B are at a distance from the foot of perpendicular drawn from the point on the l04 Apr, 2025 (M)Line in Space
  41. 41Let the values of p , for which the shortest distance between the lines and is , be , . Then the length of the latus rectum of the ellipse i04 Apr, 2025 (E)Line in Space
  42. 42Let be the point of intersection of the lines and . Let and be the point on the lines and respectively such that . Then the square of the ar04 Apr, 2025 (E)Line in Space
  43. 43Let a line passing through the point intersect the line at the point and the line at the point . Then is equal to03 Apr, 2025 (M)Line in Space
  44. 44Line passes through the point and is parallel to Z -axis. Line passes through the point and is parallel to -axis. Let for , the shortest dis03 Apr, 2025 (M)Line in Space
  45. 45Each of the angles and that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes wi03 Apr, 2025 (E)Direction Cosines and Direction Ratios
  46. 46The distance of the point from the line along the line is03 Apr, 2025 (E)Line in Space
  47. 47Let the vertices and of the triangle lie on the line and the coordinates of the point be . If the area of the triangle is then :02 Apr, 2025 (M)Line in Space
  48. 48The line is parallel to the vector and passes through the point and the line is parallel to the vector and passes through the point . The sh02 Apr, 2025 (E)Line in Space
  49. 49If the image of the point in the line joining the points and is , then is equal to02 Apr, 2025 (E)Line in Space
  50. 50Let \( { {a}}= {i}+2 {j}+ {k}\) and \( { {b}}=2 {i}+7 {j}+3 {k} . \) Let \( {L}_1: { {r}}=(- {i}+2 {j}+ {k})+ { {a}}, {R}\) and \( {L}_2: { 29 Jan, 2025 (M)Line in Space

Frequently Asked Questions

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

This chapter includes 418 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

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

Three Dimensional Geometry has appeared in 25 of the 25 years of JEE Main papers covered here, with 418 questions across 201 papers - about 2 per paper it appears in.

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

Of the 418 questions analysed for this chapter, 30% are easy, 55% moderate and 15% tough. 2023 had the most, with 71 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 - 183 questions (44%)
  • Plane in Space - 137 questions (33%)
  • Line and Plane - 72 questions (17%)
  • Line in Space has produced the most tough questions (24).
6.Is Three Dimensional Geometry's weightage in JEE Main going up or down?

Across all 201 papers analysed, Three Dimensional Geometry has averaged about 2.1 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.9 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.