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Mathematics - Three Dimensional Geometry

Practise 40 BITSAT previous year questions on Three Dimensional Geometry, compiled from papers spanning 2009 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty BITSAT tests.

Three Dimensional Geometry has been asked in 15 of the 16 years of BITSAT papers analysed (2009–2024), with 40 questions in all. 45% of them were easy, 40% moderate and 15% tough. Most of its questions came from 2023, with 6 questions that year. In the last three years (2022–2024) it had 11 questions across 6 papers, about 1.8 per paper.

The chapter's 5 topics are not weighted equally: Line and Plane (15 questions, 38%), Line in Space (11 questions, 28%), and Direction Cosines and Direction Ratios (6 questions, 15%) have been asked the most. Over the last five years the most frequent topics have been Line in Space (5), Line and Plane (4), and Basics of point in 3 dimension (2). Line and Plane has produced the most tough questions (4).

  1. 1Let the foot of perpendicular from a point to the straight line be . Let a line be drawn from parallel to the plane which meets at point . I2024 (Memory Based Paper 1)Line and Plane
  2. 2The angle between the lines whose direction cosines are given by the equations is2024 (Memory Based Paper 2)Direction Cosines and Direction Ratios
  3. 3Let the acute angle bisector of the two planes and be the plane . Then which of the following points lies on P?2024 (Memory Based Paper 2)Plane in Space
  4. 4The magnitude of projection of line joining , and on the line joining and is2024 (Memory Based Paper 3)Line in Space
  5. 5The ratio in which the YZ-plane divide the line segment formed by joining the points and is . The value of is2023 (Memory Based Paper 1)Basics of point in 3 dimension
  6. 6The lines and are coplanar if2023 (Memory Based Paper 1)Line and Plane
  7. 7The shortest distance between the lines and is :2023 (Memory Based Paper 1)Line in Space
  8. 8If the co-ordinates of the point in which the line joining the points and is intersected by the plane is , then2023 (Memory Based Paper 2)Basics of point in 3 dimension
  9. 9If the straight lines and intersect at a point, then the integer is equal to2023 (Memory Based Paper 2)Line in Space
  10. 10The shortest distance between the lines and is2023 (Memory Based Paper 2)Line in Space
  11. 11If the plane is parallel to the line , then the value of is2022Line and Plane
  12. 12The length of the perpendicular drawn from the point to the line is :2021Line in Space
  13. 13A line makes angles of and with the positive axes of and respectively. The angle made by the same line with the positive axis of , is2021Direction Cosines and Direction Ratios
  14. 14The distance from the point (3,4,5) to the point where the line meets the plane is2020Line and Plane
  15. 15The equation of plane containing line x - y = 1 , z = 1 and parallel to x 2 - z 3 = 1 , y = 3 is2019Line and Plane
  16. 16The angle between the lines whose direction cosine satisfy the equations l + m + n = 0 and l 2 = m 2 + n 2 is2019Direction Cosines and Direction Ratios
  17. 17An equation of plane parallel to plane x - 2 y + 2 z - 5 = 0 and at a unit distance from the origin is2019Plane in Space
  18. 18Reflection of the line x - 1 - 1 = y - 2 3 = z - 4 1 in the plane x + y + z = 7 is2019Line and Plane
  19. 19A line makes angles , , with the coordinate axes. If + = 2 , then cos + cos + cos 2 is equal to2018Direction Cosines and Direction Ratios
  20. 20If the sum of squares of distances of a point from the planes x + y + z = 0 , x - z = 0 and x - 2 y + z = 0 is p 2 then locus of the point i2018Plane in Space
  21. 21Line x + 1 = y - 1 = z + 2 - 4 is perpendicular to 2 x + 2 y - 8 z + 5 = 0 , then is2018Line and Plane
  22. 22If the planes r 2 i ^ - j ^ + 3 k ^ = 0 and r i ^ + 5 j ^ - k ^ = 5 are perpendicular to each other, then the value of 2 + is2018Plane in Space
  23. 23If is the angle between the vectors 4 i ^ - k ^ and i ^ + j ^ + k ^ , then sin + cos equals to2018Direction Cosines and Direction Ratios
  24. 24The length of perpendicular drawn from the point ( 2 , 3 , 4 ) to line 4 - x 2 = y 6 = 1 - z 3 , is2017Line in Space
  25. 25The image of the point ( 1 , 6 , 3 ) in the line x 1 = y - 1 2 = z - 2 3 is2017Line in Space
  26. 26The distances of the point ( 1 , - 5 , 9 ) from the plane x + y + z = 5 measured along a straight line x = y = z is 2 3 k , then the value o2017Plane in Space
  27. 27Two lines are coplanar. Then, take value (s)2015Line in Space
  28. 28A line makes the same angle with each of the and -axes. If the angle , which it makes with Y-axis, is such that then equals2015Direction Cosines and Direction Ratios
  29. 29Find the angle between the line and the plane2014Line and Plane
  30. 30The equation of the right bisector plane of the segment joining (2,3,4) and (6,7,8) is2014Line in Space
  31. 31The coordinates of the point where the line through the points and crosses the XY-plane are2013Line and Plane
  32. 32Find the angle between the two planes and2013Plane in Space
  33. 33What is the value of so that the angle between the lines having direction ratios (1,1,1) and is2012Line in Space
  34. 34The foot of the perpendicular from the point (7,14,5) to the plane are2012Line and Plane
  35. 35Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane2012Line and Plane
  36. 36Gives the line \(L: {x-1}{3}= {y+1}{2}= {z-3}{-1}\) and the plane \( : x-2 y-z=0\). Of the following assertions, the only one that is always2011Line and Plane
  37. 37If the middle points of sides \( {BC}, {CA} ~\&~ {AB}\) of triangle \(A B C\) are respectively \(D, E, F\) then position vector of centre of2010Line in Space
  38. 38The perpendicular distance of \(P(1,2,3)\) from the line \( {x-6}{3}= {y-7}{2}= {z-7}{-2}\) is2010Line and Plane
  39. 39Solution of the differential equation \( {d y}{d x}+ {y}{x}= x\) is2009Line and Plane
  40. 40If the line \( {x-4}{1}= {y-2}{1}= {z-k}{2}\) lies in the plane \(2 x-4 y+z=7\), then the value of \(k\) is2009Line and Plane

Frequently Asked Questions

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

This chapter includes 40 questions compiled from BITSAT papers spanning 2009 to 2024.

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

These are BITSAT 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 BITSAT Mathematics?

Three Dimensional Geometry has appeared in 15 of the 16 years of BITSAT papers covered here, with 40 questions across 18 papers - about 2 per paper it appears in.

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

Of the 40 questions analysed for this chapter, 45% are easy, 40% moderate and 15% tough. 2023 had the most, with 6 questions.

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

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

  • Line and Plane - 15 questions (38%)
  • Line in Space - 11 questions (28%)
  • Direction Cosines and Direction Ratios - 6 questions (15%)
  • Line and Plane has produced the most tough questions (4).
6.Is Three Dimensional Geometry's weightage in BITSAT going up or down?

Across all 18 papers analysed, Three Dimensional Geometry has averaged about 2.2 questions per paper. In the last three years (2022–2024), that average has fallen, at about 1.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.