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Mathematics - Three Dimensional Geometry

Practise 39 JEE Advanced previous year questions on Three Dimensional Geometry, compiled from papers spanning 2006 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 Advanced tests.

Three Dimensional Geometry has been asked in 19 of the 27 years of JEE Advanced papers analysed (2000–2026), with 39 questions in all. 31% of them were easy, 56% moderate and 13% tough. Most of its questions came from 2013, with 4 questions that year. In the last three years (2024–2026) it had 6 questions across 6 papers, about 1 per paper.

The chapter's 4 topics are not weighted equally: Plane in Space (18 questions, 46%), Line in Space (10 questions, 26%), and Line and Plane (10 questions, 26%) have been asked the most. Plane in Space has also led over the last five years, with 5 questions. Plane in Space has produced the most tough questions (2).

  1. 1Let be the plane such that it contains the straight line and is perpendicular to the plane . Let be the plane which passes through the point2026 (Paper 1)Plane in Space
  2. 2Let be the straight line joining the points and . Let be the foot of the perpendicular drawn from the point to the line . Another line passi2026 (Paper 2)Line in Space
  3. 3Let be the line of intersection of the planes given by the equation- Let be the line passing through the point and parallel to . Let denote 2025 (Paper 1)Line and Plane
  4. 4Let denote the three-dimensional space. Take two points and . Let denote the distance between two points and in . Let Then which of the foll2024 (Paper 1)Plane in Space
  5. 5Let be such that the lines and intersect. Let be the point of intersection of and . Let , and denote a unit normal vector to the plane conta2024 (Paper 1)Line in Space
  6. 6A straight line drawn from the point , parallel to the line , intersects the plane at the point . Another straight line which passes through2024 (Paper 2)Line and Plane
  7. 7Let Q be the cube with the set of vertices x 1 , x 2 , x 3 3 : x 1 , x 2 , x 3 0 , 1 . Let F be the set of all twelve lines containing the d2023 (Paper 1)Line in Space
  8. 8Let 1 and 2 be the lines r 1 = i ^ + j ^ + k ^ and r 2 = j ^ - k ^ + i ^ + k ^ , respectively, Let X be the set of all the planes H that con2023 (Paper 1)Plane in Space
  9. 9Let P 1 and P 2 be two planes given by P 1 : 10 x + 15 y + 12 z - 60 = 0 , P 2 : - 2 x + 5 y + 4 z - 20 = 0 . Which of the following straigh2022 (Paper 1)Plane in Space
  10. 10Let S be the reflection of a point Q with respect to the plane given by r = - t + p i ^ + t j ^ + 1 + p k ^ where t , p are real parameters 2022 (Paper 1)Plane in Space
  11. 11Let L 1 and L 2 be the following straight lines. L 1 : x 1 1 = y 1 = z 1 3 and L 2 : x 1 3 = y 1 = z 1 1 Suppose the straight line L : x l =2020 (Paper 1)Line in Space
  12. 12Let , , , be real numbers such that 2 + 2 + 2 0 and + = 1 . Suppose the point 3 , 2 , - 1 is the mirror image of the point 1 , 0 , - 1 with 2020 (Paper 2)Plane in Space
  13. 13Let L 1 and L 2 denotes the lines r = i ^ + - i ^ + 2 j ^ + 2 k ^ , R and r = 2 i ^ - j ^ + 2 k ^ , R respectively. If L 3 is a line which i2019 (Paper 1)Line in Space
  14. 14Three lines are given by r = i ^ , R r = i ^ + j ^ , R and r = i ^ + j ^ + k ^ , R . Let the lines cut the plane x + y + z = 1 at the points2019 (Paper 1)Line and Plane
  15. 15Three lines L 1 : r = i ^ , R , L 2 : r = k ^ + j ^ , R and L 3 : r = i ^ + j ^ + k ^ , R are given. For which point(s) Q and L 2 can we fin2019 (Paper 2)Line in Space
  16. 16Let P 1 : 2 x + y - z = 3 a n d P 2 : x + 2 y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?2018 (Paper 1)Plane in Space
  17. 17Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment P Q is perpendicular to the plane x + 2018 (Paper 2)Plane in Space
  18. 18The equation of the plane passing through the point ( 1,1 , 1 ) and perpendicular to the planes 2 x + y - 2 z = 5 and 3 x - 6 y - 2 z = 7 is2017 (Paper 2)Plane in Space
  19. 19Consider a pyramid O P Q R S located in the first octant x 0 , y 0 , z 0 with O , as origin, and O P and, O R along the x a x i s and the y 2016 (Paper 1)Plane in Space
  20. 20Let P be the image of the point ( 3 , 1 , 7 ) with respect to the plane x - y + z = 3 . Then the equation of the plane passing through P and2016 (Paper 2)Plane in Space
  21. 21In R 3 , consider the planes P 1 : y = 0 and P 2 : x + z = 1 . Let P 3 , be a plane, different from P 1 and P 2 , which passes through the i2015 (Paper 1)Plane in Space
  22. 22In R 3 , let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two plane2015 (Paper 1)Plane in Space
  23. 23From a point P , , , perpendiculars PQ and PR are drawn respectively on the lines y = x , z = 1 and y = - x , z = - 1 . If P is such that Q 2014 (Paper 1)Line in Space
  24. 24Perpendiculars are drawn from points on the line x + 2 2 = y + 1 - 1 = z 3 to the plane x + y + z = 3 . The feet of perpendiculars lie on th2013 (Paper 1)Line and Plane
  25. 25A line l passing through the origin is perpendicular to the lines l 1 : 3 + t i ^ + - 1 + 2 t j ^ + 4 + 2 t k ^ , - t l 2 : 3 + 2 s i ^ + 3 2013 (Paper 1)Line in Space
  26. 26Two lines L 1 : x = 5 , y 3 - = z - 2 and L 2 : x = , y - 1 = z 2 - are coplanar. Then can take value(s)2013 (Paper 2)Line in Space
  27. 27Consider the lines L 1 : x - 1 2 = y - 1 = z + 3 1 , L 2 : x - 4 1 = y + 3 1 = z + 3 2 and the planes P 1 : 7 x + y + 2 z = 3 , P 2 : 3 x + 2013 (Paper 2)Line and Plane
  28. 28The point is the intersection of the straight line joining the points and with the plane . If is the foot of the perpendicular drawn from th2012 (Paper 1)Line and Plane
  29. 29The equation of a plane passing through the line of intersection of the planes and and at a distance from the point is2012 (Paper 2)Plane in Space
  30. 30If the straight lines and are coplanar, then the plane (s) containing these two lines is (are)2012 (Paper 2)Line and Plane
  31. 31Equation of the plane containing the straight line and perpendicular to the plane containing the straight lines and is2010 (Paper 1)Plane in Space
  32. 32If the distance between the plane and the plane containing the lines and is , then is2010 (Paper 1)Plane in Space
  33. 33If the distance of the point from the plane , where , is 5 , then the foot of the perpendicular from to the plane is2010 (Paper 2)Plane in Space
  34. 34Let be a point in space and be a point on the line . Then, the value of for which the vector is parallel to the plane is2009 (Paper 1)Line and Plane
  35. 35A line with positive direction cosines passes through the point and makes equal angles with the coordinate axes. The line meets the plane at2009 (Paper 2)Line and Plane
  36. 36Paragraph: Consider the lines: Question: The shortest distance between and is2008 (Paper 2)Line in Space
  37. 37Paragraph: Consider the lines: Question: The distance of the point from the plane passing through the point and whose normal is perpendicula2008 (Paper 2)Line and Plane
  38. 38Consider the planes and . Statement I The parametric equations of the line of intersection of the given planes are and . Statement II The ve2007 (Paper 2)Direction Cosines and Direction Ratios
  39. 39A plane passes through and is perpendicular to two planes and , then the distance of the plane from the point is2006Plane in Space

Frequently Asked Questions

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

This chapter includes 39 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Three Dimensional Geometry has appeared in 19 of the 21 years of JEE Advanced papers covered here, with 39 questions across 29 papers - about one per paper it appears in.

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

Of the 39 questions analysed for this chapter, 31% are easy, 56% moderate and 13% tough. 2013 had the most, with 4 questions.

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

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

  • Plane in Space - 18 questions (46%)
  • Line in Space - 10 questions (26%)
  • Line and Plane - 10 questions (26%)
  • Plane in Space has produced the most tough questions (2).
6.Is Three Dimensional Geometry's weightage in JEE Advanced going up or down?

Across all 29 papers analysed, Three Dimensional Geometry has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.